ADVANCED PHYSICS COURSE CHAPTER 2: NEWTON’S LAWS FOR HIGH SCHOOL PHYSICS CURRICULUM AND ALSO THE PREPARATION OF ACT, DSST, AND AP EXAMS This is a complete video-based high school physics course that includes videos, labs, and hands-on learning. You can use it as your core high school physics curriculum, or as a college-level test prep course. Either way, you’ll find that this course will not only guide you through every step preparing for college and advanced placement exams in the field of physics, but also give you in hands-on lab practice so you have a full and complete education in physics. Includes text reading, exercises, lab worksheets, homework and answer keys. BY AURORA LIPPER ∙ SUPERCHARGED SCIENCE 2017
Transcript
A D V A N C E D P H Y S I C S C O U R S E
C H A P T E R 2 :
N E W T O N ’ S L A W S
FOR HIGH SCHOOL PHYSICS CURRICULUM AND ALSO THE PREPARATION OF ACT, DSST, AND AP EXAMS
This is a complete video-based high school physics course that includes videos, labs, and hands-on learning. You can use it as your core high school physics curriculum, or as a college-level test prep course. Either way, you’ll find that this course will not only guide you through every step preparing for college and advanced placement exams in the field of physics, but also give you in hands-on lab practice so you have a full and complete education in physics. Includes text reading, exercises, lab worksheets, homework and answer keys.
BY AURORA LIPPER ∙ SUPERCHARGED SCIENCE 2017
TABLE OF CONTENTS
Material List ........................................................................................................................................................................................... 4
Newton’s First Law of Motion........................................................................................................................................................ 6
Newton’s First Law of Motion........................................................................................................................................................ 7
Newton’s Law of Motion in Detail ............................................................................................................................................. 11
Inertia in Real Life ............................................................................................................................................................................ 22
Introducing the Idea of Net Forces ........................................................................................................................................... 28
Four Fundamental Forces ............................................................................................................................................................ 37
Types of Forces ................................................................................................................................................................................. 40
Resultant Force ................................................................................................................................................................................. 41
Using Vectors and Trig in Physics Problems ........................................................................................................................ 44
Force fields .......................................................................................................................................................................................... 45
Weight & Mass ................................................................................................................................................................................... 47
Gravity on Other Planets ............................................................................................................................................................... 48
Force and Mass Units ...................................................................................................................................................................... 55
Types of Friction ............................................................................................................................................................................... 57
Static and Kinetic Friction ............................................................................................................................................................ 58
Newton’s Second Law of Motion ............................................................................................................................................... 65
Newton’s Second Law with Vector Addition ........................................................................................................................ 66
Air Resistance .................................................................................................................................................................................... 67
Drag Force ........................................................................................................................................................................................... 69
Newton’s Third Law of Motion ................................................................................................................................................... 77
Third Law Explained ....................................................................................................................................................................... 82
Inertia and the Second and Third Law .................................................................................................................................... 83
Forces Come in Pairs ...................................................................................................................................................................... 83
Sled Problem ...................................................................................................................................................................................... 86
Reference Frames and the Truck Problem ........................................................................................................................... 87
Rubber Tire Problem ...................................................................................................................................................................... 88
Using Newton’s Laws Together ................................................................................................................................................. 89
Chandelier Problem ........................................................................................................................................................................ 90
Pulley Problem .................................................................................................................................................................................. 92
How to Gain and Lose Weight ..................................................................................................................................................... 93
Homework Problems with Solutions....................................................................................................................................... 94
MATERIAL LIST
While you can do the entire course entirely on paper, it’s not really recommended since physics is based in real-world observations and experiments! Here’s the list of materials you need in order to complete all the experiments in this unit.
Please note: you do not have to do ALL the experiments in the course to have an outstanding science education. Simply pick and choose the ones you have the interest, time and budget for. ball
plastic cup
hard covered book
toilet paper tube
can of chicken broth
can of clam chowder
rope (at least 3 feet long is good)
2 business card magnets
Scale
7-9″ balloon
water bottle with a sport-top (you can also use the top from liquid dish soap)
old CD
paper cup (or index card)
thumbtack
hot glue gun
razor with adult help
about 5 different shoes
board, or a tray, or a large book at least 15 inches long and no more than 2 feet long.
6 inch long piece of 2 x 4 wood, or a heavy book
spring scale (or a rubber band and a ruler)
about 5 different surfaces (table tops, carpet, chairs, etc.)
ping pong ball
golf ball
wood skewer
two straws
four caps (like the tops of milk jugs)
wooden clothespin
a piece of stiff cardboard (or four popsicle sticks)
toy car
baking soda and vinegar
tape
film canister or other plastic container with a tight-fitting lid (like a mini-M&M container)
alka-seltzer or generic effervescent tablets
INTRODUCTION
In 1666 Newton did his early work on his Three Laws of Motion. To this day, those laws still hold true. There has been some allowances for really big things (like the cosmos) and for really small things (like the atom). Other than that, Newton’s Law’s are pretty much dead on.
Newton’s Laws are all they used to get the first man to the moon. They are an amazingly powerful and wonderful area of physics. I like them because evidence of them is everywhere. If something moves or can be moved, it follows Newton’s Laws. You can’t sit in a car, walk down the road, drink a glass of milk, or kick a ball without using Newton’s Laws. I also like them because they are relatively easy to understand and yet open up worlds of answers and questions. They are truly a foundation for understanding the world around you.
Newton has a famous quote that goes “If I have seen farther than others, it is because I have stood on the shoulders of giants.” One of the giants he was referring to was Galileo. Thanks to the discoveries of Galileo and others, Newton was able to make many of his own discoveries. The most famous of which are Newton’s Laws of Motion.
Newton’s three laws of motion predict the motion of virtually all objects on Earth and in space. You are about to know all of them. Newton’s Laws are all they used to launch space craft to the moon and soon you will understand them all. Pretty powerful stuff, eh?
Newton’s Three Laws of Motion are:
1. An object at rest tends to stay at rest, an object in motion tends to stay in motion unless a force acts against it.
2. Force equals mass times acceleration.
3. Every action has an equal and opposite reaction.
NEWTON’S FIRST LAW OF MOTION
Newton’s First Law is: An object at rest tends to stay at rest, an object in motion tends to stay in motion with the same speed and direction unless an unbalanced force acts on it.
At first glance Newton’s first law seems rather obvious. Especially the first part, “An object at rest tends to
stay at rest.” Well… of course. When was the last time you saw your table move across the room for no
reason? Last time you were eating your potatoes did they float off your plate and into the lamp? NO! It’s
really the second part that is an amazing statement.
Especially if you consider when the statement was made: “An object in motion tends to stay in motion.” Think
about that. When was the last time you saw an object keep moving on its own? If you push a toy car, does it
just go and go until it hits the wall? Last time you threw a ball, if your buddy missed it did it just keep sailing
down the street? No! Both objects stopped. All object stop right? Well, yes but only on a planet.
Newton’s First Law of Motion
Overview: The natural state of objects is to follow a straight line. In fact,Newton’sFirst Law of Motion
states thatobjects in motion will tend to stay in motion unless they are acted upon by an external force.
A force is a push or a pull, like pulling a wagon or pushing a car. Gravity is also a force, but it’s a one-way
force that attracts things to each another.
What to Learn: The way to change how something is moving is to give it a push or a pull. The size of the change isrelated to the strength, or the amount of "force," of the push or pull.
Materials
wagon rocks friends stopwatch meterstick or yardstick or measuring tape
Lab Time
1. Let's really figure out what this “inertia” thing from Newton's first law is all about using the wagon and friends. Pull the wagon down the sidewalk.
2. Try to stop as quickly as you can. Be careful. You could get run over by the wagon if you’re not careful.
3. Put a friend in the wagon and repeat steps above.
4. Put another friend in the wagon and repeat again.
You may have noticed that the more friends (the more weight) you had in the wagon the harder it
was to get moving and the harder it was to stop. This is inertia. The more weight something has the
more inertia it has and the harder it is to get it to go and to stop!
Newton’s First Law of Motion Data Table
Number of Kids in Wagon Time to Stop Distance to Stop
(measure in seconds) (measure in feet or meters)
Reading
What happens when you kick a soccer ball? The ”kick” is the external force that Newton was talking
about in his first law of motion. What happens to the ball after you kick it? The ball continues in a
straight line as long as it can, until air drag, rolling resistance, and gravity, all of which cause it to stop.
If this seems overly simplistic, just stick with me for a minute. The reason we study motion is to get a
basic understanding of scientific principles. In this experiment, the ball wants to continue in a straight
line but due to external forces like gravity, friction, and so forth, the ball’s motion will change.
Newton’s First Law of Motion also says that objects at rest will tend to stay at rest, and objects in motion
tend to stay in motion unless acted upon by an external force. You’ve seen this before – a soccer ball
doesn’t move unless you kick it. But what happens if you kick it in outer space, far from any other
celestial objects? It would travel in a straight line! What if it wasn’t a soccer ball, but a rocketship? It
would still travel in a straight line. What if the rocket was going to pass near a planet? Do you think you’d
need more or less fuel to keep traveling on your straight path? Do you see how it’s useful to study things
that seem simple at first so we can handle the harder stuff later on?
Exercises Answer the questions below:
1. What is inertia?
2. What is Newton’s First Law?
3. Will a lighter or heavier race car with the same engine win a short-distance race (like the quarter-mile)?
Answers to Exercises: Newton’s First Law of Motion
1. What is inertia? (the resistance something has to change its motion)
2. What is Newton’s First Law? (Objects at rest stay at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.)
3. Will a lighter or heavier race car with the same engine win a short-distance race (like the quarter-mile)?
NEWTON’S LAW OF MOTION IN DETAIL
The reason things stop is because of two things: the forces of gravity and friction. Without them, things would just keep going. This is why planets, comets, space shuttles, meteors and more, never stop moving. They have no air resistance (in space there’s no air and as such no friction from air) and they may or may not have much gravity pulling on them. Things in orbit (the moon, satellites, etc.) do feel the pull of Earth’s gravity but they are moving fast enough to keep falling around the Earth and not into the Earth.
Now imagine Newton sitting there in 1700, he has never seen a frictionless place or a place with no gravity. He’s never seen the pictures from the space shuttle of things floating around. No one’s been to the moon yet. For him to “see” the reality that in such places things would never stop moving is pure genius.
Aristotle said the natural state for most objects was to be at rest. Newton, without ever seeing any evidence to the contrary, said the natural state for a moving object was to continue moving. When you can see through what everybody has believed to be true for centuries you are a true genius (or out of your head!).
Now imagine Newton sitting there in 1700, he has never seen a frictionless place or a place with no gravity.
He’s never seen the pictures from the space shuttle of things floating around. No one’s been to the moon yet.
For him to “see” the reality that in such places things would never stop moving is pure genius.
Aristotle said the natural state for most objects was to be at rest. Newton, without ever seeing any evidence to
the contrary, said the natural state for a moving object was to continue moving. When you can see through
what everybody has believed to be true for centuries you are a true genius (or out of your head!).
Detecting the Gravitational Field
Overview: Ok, sort of a silly experiment I admit. But here’s what we’re going for –there is an invisible
force acting on you and the ball. Things don’t change the way they are moving unless a force acts on
them. When you jump, the force that we call gravity pulls you back to Earth. When you throw a ball,
something invisible acts on the ball, forcing it to slow down, turn around, and come back down. Without
that force field, you and your ball would be heading out to space right now!
What to Learn: Everywhere you go, the acceleration due to gravity will be the same. I mean that it will
work the same on Earth, on the moon, on Jupiter, etc. For a long time, we knew there was something
pulling us down (towards the center of the earth), but we didn’t know all that much about how it
worked. We thought it acted differently on different objects. For example, we thought it would make
heavier objects fall at a faster rate than lighter objects (it would make a cannon ball fall faster than an
apple). While we know that if we dropped a cannon ball on our foot and an apple on our foot, the cannon
ball would definitely hurt more, it wouldn’t necessarily fall faster!
Materials
two different-sized objects tape measure or meter stick partner
Lab Time
1. Pick your two different-sized objects.
2. Hold them both at a height of 1 meter.
3. While your partner watches, drop both objects to see which one hits the ground first.
4. Repeat the experiment at least 2 more times.
5. Make an initial conclusion (was your hypothesis correct?)
6. Pick another item (larger or smaller) and repeat the experiment.
7. Does your initial conclusion hold true?
8. Change another variable about the experiment (change the height dropped from, change the weight of the object, or the volume of the object)
Detecting the Gravitational Field Data Table 1: Testing the Mass
Use objects of the same size but different weights.
(Ping pong ball, golf ball, foam ball, crumpled up wad of paper, tin foil ball, etc.)
Trial # Mass/Weight Guess First! Which Object Will Observations:
Hit First? Which Hit First?
Conclusion:
Detecting the Gravitational Field Data Table 1: Testing the Size
Use objects of the same mass but different surface areas.
Trial # Diameter/Area Guess First! Which Object Will Observations:
Hit First? Which Hit First?
Conclusion:
Detecting the Gravitational Field Data Table 1: Testing the Height
Use objects of the same size but different weights.
(Ping pong ball, golf ball, foam ball, crumpled up wad of paper, tin foil ball, etc.)
Trial # Height Guess First! Which Object Will Observations:
Hit First? Which Hit First?
Conclusion:
Reading
Gravity is probably the force field you are most familiar with. If you’ve ever dropped something on
your foot you are painfully aware of this field! Even though we have known about this field for a
looooong time, it still remains the most mysterious field of the four.
What we do know is that all bodies, from small atoms and molecules to gigantic stars, have a
gravitational field. The more massive the body, the larger its gravitational field. As we said earlier,
gravity is a very weak force, so a body really has to be quite massive (like moon or planet size) before
it has much of a gravitational field. We also know that gravity fields are not choosy. They will attract
anything to them.
All types of bodies, from poodles to Pluto, will attract and be attracted to any other type of body.
One of the strangest things about gravity is that it is only an attractive force. Gravity, as far as we
can tell, only pulls things towards it. It does not push things away. All the other forces are both
attractive (pull things towards them) and repulsive (push things away).
Exercises Answer the questions below:
1. What did you determine about gravity and how it affects the rate of falling?
2. Did changing the object affect the rate of falling? Why or why not?
3. Did changing the variable affect the rate of falling? Why or why not?
Answers to Exercises: Detecting the Gravitational Field
1. What did you determine about gravity and how it affects the rate of falling? (Gravity appears to affect all objects the same.)
2. Did changing the object affect the rate of falling? Why or why not? (No, it appears that gravity affects all objects the same.)
3. Did changing the variable affect the rate of falling? Why or why not? (No, it appears that gravity affects all objects the same.)
INERTIA
There is a term in physics that really kind of encompasses Newton’s first law, and that is inertia. Inertia is a
quality of an object that determines how difficult it is to get that object to move, to stop moving, or to change
directions. Generally, the heavier an object is, the more inertia it has. I like to think of inertia as a mule. It is
often very hard to get a mule to move, and once you do get him moving it is very difficult to get him to stop or
to change directions!
Inertia is the tendency to resist changes in both acceleration and velocity. A hockey puck sliding on ice, or a
puck on an air hockey table, travels a lot farther than if the puck were on the street. The puck moves with little
to no friction and maintains its speed for a long time.
Ta-Daa!
Overview: Ever wonder how magicians work their magic? This experiment is worthy of the stage with a
little bit ofpractice on your end. If you believe in the laws of physics, particularly Newton’s laws, then this experiment will work every time.
Materials
plastic cup hardcover book toilet paper tube several different objects like a ball that is smaller than the cup opening, but larger than the
toilet paper tube
Lab Time
1. Put the cup on a table and put the book on top of the cup.
2. This is the tricky part. Put the toilet paper tube upright on the book, exactly over the cup.
3. Now put the ball on top of the toilet paper tube.
4. Check again to make sure the tube and the ball are exactly over the top of the cup.
5. Now, hit the book on the side so that it moves parallel to the table. You want the book to slide quickly between the cup and the tube.
6. If it works right, the book and the tube fly in the direction you hit the book. The ball however falls straight down and into the cup.
7. If it works say TAAA DAAA!
8. Draw a diagram of your experiment right before you hit the book. Label where you expect to see Newton’s three different laws in action as soon as you set things in motion:
Reading
This experiment is all about inertia. The force of your hand got the book moving. The friction between
the book and the tube (since the tube is light it has little inertia and moves easily) causes the tube to
move. The ball, which has a decent amount of weight, and as such a decent amount of inertia, is not
affected much by the moving tube. The ball, thanks to gravity, falls straight down and, hopefully, into the
cup. Remember the old magician’s trick of pulling the tablecloth and leaving everything on the table?
Now you know how it’s done. “Abra Inertia”!
Remember: inertia is how hard it is to get an object to change its motion, and Newton’s First Law
basically states that things don’t want to change their motion. Once your students get good at this,
invite them to try it with other objects, like unpeeled hardboiled eggs.
Exercises Answer the questions below:
1. What are two different pairs of forces in this experiment?
2. Explain where Newton’s Three Laws of motion are observed in this experiment.
Answers to Exercises: Ta-Daa!
1. What are two different pairs of forces in this experiment? (the force made by the hand and the force of gravity on the ball)
2. Explain where Newton’s Three Laws of motion are observed in this experiment. (This is fun to ask
the students as you walk around observing their work. Have them point out different parts of
their experiment in action.)
INERTIA IN REAL LIFE
Next time you go for a ride bring a tennis ball with you in the car. Sit in the back seat and put the tennis ball in
the seat next to you. Now watch the ball carefully as the car moves. See how it moves around the seat? (Try not
to let it get on the floor and roll around. It might roll under the pedals and that would be bad.) So, what do you
think happened and why?
As the car moves forward at 20 mph, everything in the car is moving forward at 20 mph. Everything in the car
has the same inertia. If the car were to stop suddenly, everything in the car that’s not bolted down, still moves
forward at 20 mph until it hits something. An object at rest tends to stay at rest, an object in motion tends to stay
in motion. Right? So, if the car stops quickly, the tennis ball continues to move forward until it hits something.
If the car turns, the ball continues to go in the direction it was going a second ago, so it rolls around the seat.
What would happen if the car stopped suddenly and you weren’t wearing a seat belt? Yup, you’d fly forward at
whatever speed the car was going until you crashed into something in the car. See now why seat belts are your
best friend?
Chicken and Clam
Overview: Next time you watch a car race, notice the wheels. Are they solid metal discs, or do they have
holesdrilled through the rims? I came up with this somewhat silly, but incredibly powerful quick science
demonstration to show my university students how a good set of rims could really make a difference on
the racetrack (with all other things being equal).
What to Learn: You’re going to learn about inertia, what it is and how to measure it and its effects.
Materials
clam chowder (1 can)
chicken broth (1 can)
long table
books to prop up one end of the table so it becomes a long ramp
optional: different kinds of cans of soup (note you must have the two mentioned above)
Lab Time
1. Prop up one end of a long table about 6-12″ (you can experiment with the height later).
2. You’re going to roll both soup cans down the table at the same time.
3. Which do you expect to reach to bottom first – the chicken or the clam? Write down your guess in your data table.
4. Not only do my college students need to figure out which one will win, they also have to tell me why. The secret is in how you calculate the inertia of each. Take a guess, then do the activity.
5. Place the two cans together at the top of your ramp and release them at the same time so that they roll down together.
6. Do you think the can with more inertia will win or lose?
7. Try this experiment two more times in order to validate your results.
8. Try this with different kinds of soup cans. See if you can figure out a pattern and predict the results of more trial runs for this experiment.
Chicken and Clam Data Table
Soup Can #1 Soup Can #2 Guess: Who Will Win? Who Won?
Reading
Inertia is a quality of an object that determines how difficult it is to get that object to move, to stop
moving, or to change directions. Generally, the heavier an object is, the more inertia it has. An
elephant has more inertia than a mushroom. A sumo wrestler has more inertia than a baby. Inertia
is made from the Latin word “inert,” which means “lacking the ability to move.” Inertia isn’t
something people have a grasp of, though, as it’s something you must mathematically calculate from
an object’s mass and size.
When riding in a wagon that suddenly stops, you go flying out. Why? Because an object in motion
tends to stay in motion unless acted upon by an outside force (Newton’s First Law). When you hit
the pavement, your motion is stopped by the sidewalk (external force). Seat belts in a car are
designed to keep you in place and counteract inertia if the car suddenly stops.
Did you know that Newton had help figuring out this First Law? Galileo rolled bronze balls down a
wood ramp and recorded how far each rolled during a one-second interval to discover gravitational
acceleration. And René Descartes (the great French philosopher) proposed three laws of nature, all of
which Newton studied and used in his published work.
All of these men had to overcome the longstanding publicly accepted theories that stemmed from the
Greek philosopher Aristotle (which was no small feat in those days). Aristotle had completely rejected
the idea of inertia. He also had thought that weight affected falling objects, which we now know to be
false. But remember that back then, people argued and talked about ideas rather than performing
actual experiments to discover the truth about nature. They used words and reason to navigate
through their world more than scientific experimentation.
In this experiment, the chicken soup wins for a very simple reason. Imagine that the cans are
transparent, so you can see what goes on inside the cans as they roll down the ramp. Which one has
just the can rolling down the ramp, and which has the entire contents locked together as it rolls? The
can of the chicken soup will rotate around the soup itself, while the clam chowder acts as a solid
cylinder and rotates together. So the inertial mass of the clam is much greater than the inertial mass of
the soup, even though the cans weigh the same.
How do you calculate the inertia of the chicken soup and the clam? Here’s the mathematical formulae from the back of a dynamics textbook (a typical course that all engineers take during their 2nd year of college).
Inertia of a solid cylinder = ½ (mr²)
Inertia of a cylindrical shell =1
12(𝑚𝑟2)
If the radius of the soup can is 6.5 cm and the mass for both is the same (345 grams, or 0.345kg), and the mass of an empty can is 45 grams, then:
(CLAM)
Inertia of a solid cylinder = 1
2(𝑚𝑟2) =
1
2(0.345 𝑘𝑔)(6.5 𝑐𝑚)2 = 7.29 𝑘𝑔 𝑐𝑚3
(CHICKEN)
Inertia of a cylindrical shell = 1
12(𝑚𝑟2) =
1
12(0.045 𝑘𝑔)(6.5 𝑐𝑚)2 = 1.258 𝑘𝑔 𝑐𝑚3
The numerical value for the solid cylinder is larger than the shell, which tells us that it has a greater
resistance to rolling and will start to rotate much slower than the shell. This makes logical sense, as
it’s easier to get the shell alone to rotate than move a solid cylinder. Remember, you must use the
mass of the cylinder shell (empty can) when calculating the chicken’s inertia, as the broth itself does
not rotate and this does not have a ”rolling resistance!”
Exercises Answer the questions below:
1. What is inertia (in your own words)?
2. Why does one soup can always win?
Answers to Exercises : Chicken and Clam
1. What is inertia (in your own words)? (The resistance something has to changing its motion.)
2. Why does one soup can always win? (The can of the chicken soup will rotate around the soup
itself, while the clam chowder acts as a solid cylinder and rotates together. So the inertial mass of
the clam is much greater than the inertial mass of the soup, even though the cans weigh the same.
This means that the clam chowder has more rolling resistance than the chicken broth.)
INTRODUCING THE IDEA OF NET FORCES
Forces are not needed to keep objects moving… they are the reason objects accelerate or stop moving. A ball
comes to rest because of friction. If there wasn’t friction between the ball and the grass, the ball would go on
rolling forever (or at least until the end of the field). Forces like friction bring objects to rest.
It is very rare, especially on Earth, to have an object that is experiencing force from only one direction. A
bicycle rider has the force of air friction pushing against him. He has to fight against the friction between the
gears and the wheels. He has gravity pulling down on him. His muscles are pushing and pulling inside him and
so on and so on.
Even as you sit there, you have at least two forces pushing and pulling on you. The force of gravity is pulling
you to the center of the Earth. The chair is pushing up on you so you don’t go to the center of the Earth. So with
all these forces pushing and pulling, how do you keep track of them all? That’s where net force comes in. The
net force is when you add up all of the forces on something and see what direction the overall force pushes in.
The word “net”, in this case, is like net worth or net income. It’s a mathematical concept of what is left after
everything that applies is added and subtracted. The next activity will make this clearer.
Highlights for Velocity & Newton’s First Law:
1. Newton’s First Law is an object at rest tends to stay at rest and an object in motion tends to stay in motion
unless a force acts against it.
2. Inertia is a quality of an object that determines how difficult it is to get that object to move, to stop moving or
to change directions.
3. Force is a push or a pull on something.
4. Objects tend to keep on doing what they are doing. They resist changes in their motion. The motion
continues until the object encounters an unbalanced force.
Did you see item #4 above? It mentions an unbalanced force. An unbalanced force is a force that causes an
object to move, you might say. Let’s take a closer look… stand up right now.
You are in a state of equilibrium, meaning that you’re not falling toward the center of the Earth, and you’re not
floating off into space. That’s what we mean by equilibrium: the pull of gravity is balanced by the force of the
floor pushing up on you (called the normal force). The force of gravity is toward the floor, and the force of the
floor is toward the ceiling. They are the same magnitude (if you weigh 100 pounds, then the magnitude of this
force is 100 pounds) and in opposite directions. so balance each other out, and you are not moving. A net force
of zero means that either you are not moving or not accelerating, as we’ll see in Newton’s Second Law.
Net Forces
Overview: The net force (Fnet) is when you add up all of the forces on something and see what direction theoverall force pushes in. The word “net,” in this case, is like net worth or net income. It’s a mathematical concept of what is left after everything that applies is added and subtracted.
What to Learn: Today you get to learn how unbalanced forces cause changes in velocity.
Materials
rope (about 3 feet long)
friend
sense of caution (Be careful with this. Don’t pull too hard and please don’t let go of the rope. This is fun but you can get hurt if you get silly.)
Lab Time
1. Both you and your friend grab either end of the rope. Pull it back just enough to get the rope off the ground. (scenario 1)
2. Have your friend pull harder than you are. (scenario 2)
3. You pull harder than your friend is. (scenario 3)
4. Both of you pull the rope, and try to pull with the same force. (scenario 4)
5. For scenario 1, draw a free body diagram below (the rope is your object, you are on the left, and your friend is on the right)
Reading
It is not very common for only one force to be acting on an object at one given time. In fact, at almost all
times, there are two forces acting on you! We know that gravity is always acting on us, pulling us down
towards the center of the Earth (the reason we don’t fly off into space). But if gravity was the only force
acting on us, we would be constantly falling towards the center of the Earth.
If we aren’t always falling towards the center of the Earth, what is stopping us? Of course, it is the chair
you are sitting on, or the ground you are standing on. The reason we know there is a force is, simply put:
We are NOT falling towards the center of the Earth (I know, seems a little simple, right?). There is also a
way to figure out exactly how much force the chair or ground exerts on us. We already know how to
calculate to force of gravity (FG = mg), If we are sitting or standing still, then we know the force the
chair/ground exerts has to be the exact same amount as the gravity acting on us. The only difference is
that gravity pulls us towards the center of the earth, while the force of the chair/ground pushes us away
from the center of the earth.
This is how we know Newton’s Third Law of Motion. For every action, there is an equal and opposite
reaction. In this case, for the force of gravity pulling us down there is an equal force pushing us in the
opposite direction. This force is called a normal force, because it is the normal reaction to gravity.
What this leads us to is what is known as net force. Net is a term commonly used in mathematics and
finance as a smart way to say “total.” It is the total force acting on an object at any given point in time.
Typically, you can draw the object and draw the forces pulling on the object at any given time. Don’t
worry, you don’t have to be a great artist. In fact, to keep things simple and consistent, we always draw
the object as a simple box. And we draw the forces acting on the box as an arrow, coming out from the
object NOT into the object. If any forces push/pull the object down, we draw it coming out of the bottom
of the box, anything pulling the object up coming out from the top of the box. The size of the arrow
makes a difference, too. The bigger the force, the bigger the arrow. Let’s look at how we would draw our
example of you standing on the floor below.
First, draw your object (remember, just a simple box)
Next, draw the first force (usually gravity, because it’s always there!) Don’t forget to label the force. When you get to 4 or 5 forces, labels help you remember what is what!
Now draw the second force (In this case our normal force). The magnitude of the force is the same, so the arrow should be the same size, but the direction is the opposite of the force of gravity
Our drawing makes it easy to see that there are 2 forces acting on the object, they are equal in
magnitude and opposite in direction, so there is a net force of zero acting on our object. We know
right away that our object is either not moving, or moving, but at a constant speed, so not accelerating.
We could add numbers to our diagram as well to mathematically calculate to Net Force acting on our
object. To calculate the Net Force, we simply add up all of the forces (only add y-axis forces, or x-axis forces together, not an x force and a y force) or:
FNET = F1 + F2 + F3….
Let’s say the force of gravity acting on our object is 100 N, and the normal force is also 100 N. If we add up our force to get our net force, we would get 200 N.
FNET = FG + FN
FNET = 100 N + 100 N
FNET = 200 N
That doesn’t seem right, because we know the net force is 0 N. Because the forces are vectors, we have to consider direction. When they move in opposite directions, one of them has to be negative. Typically, the downward and leftward forces are negative, and the upward and rightward forces are positive. This isn’t a rule, but an easy way to keep it consistent. So now if we add up the forces:
FNET = FG + FN
FNET = -100 N + 100 N
FNET = 0 N
We get zero for the net force, just like we already knew it should be.
Exercises:
1. For scenario 1, in which direction did you both move? Draw the free body diagram below
2. For scenario 2, in which direction did you both move? Draw the free body diagram below
3. For scenario 3, in which direction did you both move? Draw the free body diagram below
4. For scenario 4, in which direction did the rope move? Draw the free body diagram below
5. What was the same about question 1 and question 4? What was different?
6. Even though the forces were less in question 1 than question 4, what was the net force for both?
7. There were always at least 3 forces acting on the rope, what were they? Did you include the third force in your free body diagram?
8. If the rope wasn’t moving, but you had only one force moving down, what does that tell you about the force you and your friend exerted?
Net Forces Data Table
Calculations: Assume the light force (when you picked up the rope, or pulled less than your friend was 10 N. Assume the Stronger Force (when your friend pulled harder, or your pulled harder or you both pulled hard) was 75 N. If we ignore amount that counteracted gravity and assume they were both in the x-axis direction, fill in the table below. Don’t forget to consider direction.
Scenario Your Force Your friend’s Force Net Force
1 -10 N 10 N
2 -10 N 75 N
3 -75 N 10 N
4 -75 N 75 N
Answers to Exercises: Net Forces
1. For scenario 1, draw a free body diagram below (the rope is your object, you are on the left, and your friend is on the right)
2. For scenario 2, in which direction did you both move? Draw the free body diagram below (Right)
3. For scenario 3, in which direction did you both move? Draw the free body diagram below (left)
4. For scenario 4, in which direction did the rope move? Draw the free body diagram below (Didn’t move)
5. What was the same about question 1 and question 4? What was different? (The rope didn’t move.
Question 1 had small forces, Question 4 had large forces)
6. Even though the forces were less in question 1 than question 4, what was the net force for both? (Net force was zero in both cases.)
7. There were always at least 3 forces acting on the rope, what were they? Did you include the third force in your free body diagram? (2 applied forces and gravity)
8. If the rope wasn’t moving, but you had only one force moving down, what does that tell you about the force you and your friend exerted? (They had to have some portion of the force that was pulling up.)
FORCES
If I asked you to define the word force, what would you say? You probably have a feeling for what force means, but you may have trouble putting it into words. It’s kind of like asking someone to define the word “and” or “the”. Well, this lesson is all about giving you a better feeling for what the word force means. We’ll be talking a lot about forces in many lessons to come. The simplest way to define force is to say that it means a push or a pull like pulling a wagon or pushing a car. That’s a correct definition, but there’s a lot more to what a force is than just that.
FOUR FUNDAMENTAL FORCES
There are four types of forces. They are, in order of strength, strong nuclear force, electromagnetism, weak
nuclear force, and gravity. That’s it. Those are all the forces that do all the pushing and pulling in the entire
universe. The strong and weak nuclear forces are responsible for holding atoms together. They are quite
important, but unless you’re dealing with physics at a quantum (atomic) level they are not something you need
to know too much about. So we won’t spend any time on them here.
As you look at the list of the fearsome foursome of forces, you may notice a couple of strange things. The first
thing you may have asked yourself is, “Gravity is the weakest force!!??” Believe it or not, of all the forces,
gravity is the weakling. It is actually much weaker than the other three. In fact, the other three have a tendency
to pick on gravity, which isn’t very nice.
Some other questions you might be thinking are “Where is friction in the list?” and “What about pulling a
wagon, what kind of force is that?” Excellent questions my perceptive pupil! Here comes a bit of a shocker.
Friction, which is what allows you to pull a wagon, push a car, and sit in your chair without sliding off, is
actually an electromagnetic force. You can sit in your chair because there are electromagnetic interactions
between the atoms in your, uh…rear section, and the atoms in the chair. In fact, you aren’t touching that chair.
Or I should say, your matter is not touching the matter of the chair. The electromagnetic fields around your
atoms and the chair’s atoms are touching but particles of matter are not. This fact comes in very handy when
you’re in the back of the car with your brother or sister and they yell, “Will you STOP touching me!” Now you
can say with great smugness, “I’m not touching you, only my electromagnetic forces are!” Isn’t physics fun?
As for pulling a wagon, you can think of yourself as a living, breathing electromagnetic force maker. When you
pull a wagon, you are using electromagnetic force to work your muscles and do what needs to be done to get
that wagon going.
Stick and Slip
Overview: Friction is everywhere! Imagine what the world would be like without friction! Everything
you do, from catching baseballs to eating hamburgers, to putting on shoes, friction is a part of it. If you
take a quick look at friction, it is quite a simple concept of two things rubbing together.
What to Learn: When you take a closer look at friction, it’s really quite complex. What kind of surfaces
are rubbing together? How much of the surfaces are touching? And what’s the deal with this stick and
slip thing anyway? Friction is a concept that many scientists are spending a lot of time on. Understanding
friction is very important in making engines and machines run more efficiently and safely.
Materials
magnets (2, business-card sized)
fingers
Lab Time
1. Take two business card magnets and stick them together, black magnet side to black magnet side. They should be together so that the pictures are on the outside like two pieces of bread on a sandwich.
2. Now grab the sides of the magnets and drag one to the right and the other to the left so that they still are magnetically stuck together as they slide over one another.
3. Did you notice what happened as they slid across one another? They stuck and slipped didn’t
they? This is a bit like friction. As two surfaces slide across one another, they chemically bond and
then break apart. Bond and break, bond and break as they slide. The magnets magnetically
“bonded” together and then broke apart as you slid them across on another. The chemical bonds
don’t work quite like the magnetic “bonds” but it gives a decent model of what’s happening.
Exercises Answer the questions below:
1. What is the difference between static and kinetic friction? Which one is always greater?
2. Design an experiment where you can observe and/or measure the difference between static and kinetic friction.
Answers to Exercises: Stick and Slip
1. What is the difference between static and kinetic friction? Which one is always greater? (Static
friction is always greater, since it takes more energy to start an object moving from rest. Static
friction is the friction you need to overcome in order to start an object sliding. Kinetic friction is
the friction after an object is in motion.)
2. Design an experiment where you can observe and/or measure the difference between static and
kinetic friction. (Place an object on a ramp. Raise the ramp until the object starts to slide (static
friction). Notice that you have to lower the incline just a bit to keep it sliding at a constant rate
(kinetic friction). You can also take a rubber band and attach it to an object at rest on the ground.
Measure the rubber band’s length the moment the object starts to slide, and then also when it’s
sliding at a constant rate. You’ll notice that the rubber band is longer when it’s overcoming static
friction and starting to slide.)
TYPES OF FORCES
There are two big categories that forces fall into: contact forces, and forces resulting from something called action-at-a-distance, like gravitational, magnetic, and electrical forces. Contact forces come into play when objects are physically touching each other, like friction, air resistance, tension, and applied forces (like when your hand pushes on something, or you kick a ball with your foot). Action-at-a-distance forces show up when the sun and planets pull on each other gravitationally. The sun isn’t in contact with the Earth, but they still exert a force on each other. Two magnets repel each other even though they don’t touch… that’s another example of action-at-a-distance force. Inside an atom, the protons and the electrons pull on each other via the electrical force. The units of force are in “Newtons”, or N like this: “my suitcase weighs 20N”. 1 N = 1 kg * m/s2. A force is also a vector, meaning that is has magnitude and direction. The force my suitcase exerts on the ground is 20N in the downward direction. Scientists and engineers use arrows to indicate the direction of force. We’ll learn how to do this by drawing “Free Body Diagrams”, or FBDs. These are really useful for inventors and engineers, because with one look at a structure or machine, they can see all the forces acting on it and quickly be able to tell if the object is experiencing unbalanced forces, and if so what would happen. Unbalanced forces can cause rockets to crash, aircraft to somersault, bridges to collapse, trains to roll off the track, skyscrapers to topple, machines to explode or worse! We’re going to learn how to see forces by making a model of the real world down on paper, drawing in all the forces acting on the object and use a little math to figure out important information like acceleration, force and velocity. Most engineers and scientists spend a year or more studying just this one concept about FBDs (and also MADs: “Mass-Acceleration Diagrams”) in college, so let’s get started…
RESULTANT FORCE
In order to figure out what’s going on with an object, you have to take a look at the forces being applied to it. Forces are a vector, meaning that they have a direction and a magnitude. Your weight is not just a number, but it’s also in the downward direction. When we look at the forces that act on an object (or system of objects), we need to know how to combine all the forces into a single, resultant force which makes our math a lot easier. Here’s a set of videos that will show you how to do this:
PRACTICING RESULTANT FORCES
Now let’s take it a step further and look at how you’d analyze a ball being yanked on by two kids in different directions:
VECTOR NOTATION & TRIGONOMETRY
There’s a different type of notation for x and y axes called “i-hat” and “j-hat”. This next video will show you exactly what you need to know to understand how to use them together so you don’t get confused! If you haven’t learned about “sines” or “cosines” yet, or it’s been awhile since you’ve studied triangles, this video will show you exactly what you need to know in order to solve physics problems. We’re not going to spend time deriving where these came from (if you’re interested in that, just open up a trigonometry textbook), but rather we’re going to learn how to use them in a way that real scientists and engineers do. Take out your notebook and take notes on the law of sines, law of cosines, and write down definitions for sine, cosine, and tangent based on what you learn in the video, especially if you’re new to all this. Take it slow and you’ll catch on soon enough, because math isn’t just a shiny box of tools you just learn about, but you need to take the tools out of the box and learn how to crank with them. And sometimes, you learn how to use a impact driver when you need it, not ahead of time for someday when you might need it. Don’t get stuck if you haven’t seen some of these math principles yet or if they don’t make sense where they came from – just start using them and your brain will pick it up on the way as you learn how to apply them. Again, don’t feel like you have to complete a comprehensive course in trig to be able to figure out how to add vectors together! Just follow these simple steps…
USING VECTORS AND TRIG IN PHYSICS PROBLEMS
Now let’s put the coordinate systems together with vector addition into this more realistic problem we’re going to run into with our study in physics:
FORCE FIELDS
Force fields aren’t just something for science fiction writers. They are actually a very real and very mysterious part of the world in which you live. So, what is a force field? Well, I can’t tell you. To be honest, nobody can. There’s quite a bit that is still unknown about how they work. A force field is a strange area that surrounds an object. That field can push or pull other objects that wander into its area. Force fields can be extremely tiny or larger than our solar system. A way to picture a force field is to imagine an invisible bubble that surrounds a gizmo. If some other object enters that bubble, that object will be pushed or pulled by an invisible force that is caused by the gizmo. That’s pretty bizarre to think about isn’t it? However, it happens all the time. As you sit there right now, you are engulfed in at least two huge force fields, the Earth’s magnetic field and the Earth’s gravitational field. Gravity doesn’t care what size something is or whether or not it is moving, Gravity treats all things equally and accelerates them the same. Notice, that I say gravity accelerates all things equally, not gravity pulls on all things equally. Gravity does pull harder on some things than on other things. This is why I weigh more than a dog. I am made of more stuff (I have more atoms) than the average dog, so gravity pulls on me more. Weight is nothing more than a measure of how much gravity is pulling on you. This is why you can be “weightless” on a scale in space. You are still made of stuff, but there’s a balance of the gravity that is pulling on you and the outward force due to the acceleration since you’re moving in a circle (which you do in order to remain in orbit), so it feels like you have no weight.
GRAVITATIONAL FIELDS & WEIGHTLESSNESS
The larger a body is, the more gravitational pull or the larger a gravitational field it will have. The Moon has a fairly small gravitational field (if you weighed 100 pounds on Earth, you’d only be 17 pounds on the Moon), the Earth’s field is fairly large and the Sun has a HUGE gravitational field (if you weighed 100 pounds on Earth, you’d weigh 2,500 pounds on the sun!). As a matter of fact, both the dog and I both have gravitational fields! Since we are both bodies of mass we have a gravitational field which will pull things towards us. All bodies have a gravitational field. However, my mass is sooooo small that the gravitational field I have is miniscule. Something has to be very massive before it has a gravitational field that noticeably attracts another body. So what’s the measurement for how much stuff you’re made of? Mass. Mass is basically a weightless measure of how much matter makes you, you. A hamster is made of a fairly small amount of stuff so she has a small mass. I am made of more stuff, so my mass is greater than the hamster’s. Your house is made of even more stuff so its mass is greater still. So, here’s a question. If you are “weightless” in space, do you still have mass? Yes, the amount of stuff you’re made of is the same on Earth as it is in your space ship. Mass does not change but since weight is a measure for how much gravity is pulling on you, weight will change. Did you notice that I put weightless in quotation marks? Wonder why? Weightlessness is a myth! Believe it or not, one is never weightless. A person can be pretty close to weightless in very deep space but the astronauts in a space ship actually do have a bit of weight. Think about it for a second. If a space ship is orbiting the Earth what is it doing? It’s constantly falling! If it wasn’t moving forward at 10’s of thousands of miles an hour it would hit the Earth. It’s moving fast enough to fall around the curvature of the Earth as it falls but, indeed, it’s falling as the Earth’s gravity is pulling it to us. Otherwise the ship would float out to space. So what is the astronaut doing? She’s falling too! The astronaut and the space ship are both falling to the Earth at the same rate of speed and so the astronaut feels weightless in space. If you were in an elevator and the cable snapped, you and the elevator would fall to the Earth at the same rate of speed. You’d feel weightless! (Don’t try this at home!)
WEIGHT & MASS
The difference between weight and mass often trips up college students, so let’s straighten this out. The mass of an object is how much stuff something is made out of, and the weight is the force of gravity acting on it. Mass deals with how much stuff there is, and weight deals with the pull of the Earth. Mass will never change no matter where you put the object, unless you take a bite out of it or pile more stuff on top of it. The weight can change depending on where you place it, like on another planet.
GRAVITY ON OTHER PLANETS
Let’s do an example: a 10 kg suitcase weighs 98.1N on Earth, but only 16.2N on the moon (the gravitational
acceleration on the moon is 1.622 m/s2 ). On the moon, the mass of the suitcase is still the same 10 kg unless I
take out clothes or put in a bowling ball. However, the weight of the suitcase will change depending on which
planet I visit. Weight will change depending on the acceleration of gravity on each planet. It also varies
depending on how close or far I am from the planet or object (like the sun). The further from the object, the less
the pull of gravity. Neptune experiences a less pull from the sun than the Earth does. How about other planets?
Watch Your Weight
Overview: If you could stand on the Sun without being roasted, how much would you weigh? The
gravitational pullis different for different objects. Let’s find out which celestial object you’d crack the
pavement on, and which your lightweight toes would have to be careful about jumping on in case you leapt off the planet.
What to Learn: Weight is nothing more than a measure of how much gravity is pulling on you. Mass is a
measureof how much stuff you’re made out of. Weight can change depending on the gravitational field
you are standing in. Mass can only change if you lose an arm.
Materials
Scale to weigh yourself
Calculator
Pencil
Experiment
1. We need to talk about the difference between weight and mass. In everyday language, weight and mass are used interchangeably, but scientists know better.
2. Mass is how much stuff something is made out of. If you’re holding a bowling ball, you’ll notice that
it’s hard to get started, and once it gets moving, it needs another push to get it to stop. If you leave
the bowling ball on the floor, it stays put. Once you push it, it wants to stay moving. This
“sluggishness” is called inertia. Mass is how much inertia an object has.
3. Every object with mass also has a gravitational field, and is attracted to everything else that has
mass. The amount of gravity something has depends on how far apart the objects are. When you
step on a bathroom scale, you are reading your weight, or how much attraction is between you
and the Earth.
4. If you stepped on a scale in a spaceship that is parked from any planets, moons, black holes, or
other objects, it would read zero. But is your mass zero? No way. You’re still made of the same
stuff you were on Earth, so your mass is the same. But you’d have no weight.
5. What is your weight on Earth? Let’s find out now.
6. Step on the scale and read the number. Write it down.
7. Now, what is your weight on the Moon? The correction factor is 0.17. So multiply your weight by 0.17 to find what the scale would read on the Moon.
8. For example, if I weigh 100 pounds on Earth, then I’d weight only 17 pounds on the Moon. If the scale reads 10 kg on Earth, then it would read 1.7 kg on the Moon
Watch Your Weight Data Table
Weight on Planet/Object = Weight on Earth x Gravity Correction
Planet/Object Weight on Earth Gravity Correction
Weight on
Planet/Object
The Sun 28
Mercury 0.38
Venus 0.91
Earth 1
Moon 0.17
Mars 0.38
Jupiter 2.14
Saturn 0.91
Uranus 0.86
Neptune 1.1
Reading
Weight is nothing more than a measure of how much gravity is pulling on you. This is why you can be
“weightless” in space. You are still made of stuff, but there’s no gravity to pull on you so you have no
weight. The larger a body is, the more gravitational pull (or in other words the larger a gravitational
field) it will have.
The Moon has a fairly small gravitational field (if you weighed 100 pounds on Earth, you’d only be 17
pounds on the Moon).The Earth’s field is fairly large and the Sun has a HUGE gravitational field (if you
weighed 100 pounds on Earth, you’d weigh 2,500 pounds on the Sun!).
As a matter of fact, the dog and I both have gravitational fields! Since we are both bodies of mass, we
have a gravitational field which will pull things toward us. All bodies have a gravitational field.
However, my mass is so small that the gravitational field I have is miniscule. Something has to be very
massive before it has a gravitational field that noticeably attracts another body.
So what’s the measurement for how much stuff you’re made of? Mass. Mass is basically a weightless
measure of how much matter makes you you. A hamster is made of a fairly small amount of stuff, so she
has a small mass. I am made of more stuff, so my mass is greater than the hamster’s. Your house is made
of even more stuff, so its mass is greater still. So, here’s a question. If you are “weightless” in space, do
you still have mass? Yes, the amount of stuff you’re made of is the same on Earth as it is in your space
Pluto 0.08
Outer Space 0
Betelgeuse 14,000
White Dwarf 1,300,000
Neutron Star (Pulsar) 140,000,000,000
Black Hole ∞
ship. Mass does not change, but since weight is a measure for how much gravity is pulling on you, weight
will change.
Did you notice that I put weightless in quotation marks? Wonder why?
Weightlessness is a myth! Believe it or not, one is never weightless. A person can be pretty close to weightless in very deep space, but the astronauts in a space ship actually do have a bit of weight.
Think about it for a second. If a space ship is orbiting the Earth, what is it doing? It’s constantly falling! If
it wasn’t moving forward at tens of thousands of miles an hour it would hit the Earth. It’s moving fast
enough to fall around the curvature of the Earth as it falls but, indeed, it’s falling as the Earth’s gravity is pulling it to us.
Otherwise the ship would float out to space. So what is the astronaut doing? She’s falling, too! The
astronaut and the space ship are both falling to the Earth at the same rate of speed and so the astronaut
feels weightless in space. If you were in an elevator and the cable snapped, you and the elevator would
fall to the Earth at the same rate of speed. You’d feel weightless! (Don’t try this at home!)
Either now, or at some point in the future you may ask yourself this question, “How can gravity pull
harder (put more force on some things, like bowling balls) and yet accelerate all things equally?” When
we get into Newton’s laws in a few lessons, you’ll realize that doesn’t make any sense at all. More force
equals more acceleration is basically Newton’s Second law.
Well, I don’t want to take too much time here since this is a little deeper then we need to go but I do feel
some explanation is in order to avoid future confusion. The explanation for this is inertia. When we get
to Newton’s First law we will discuss inertia. Inertia is basically how much force is needed to get
something to move or stop moving.
Now, let’s get back to gravity and acceleration. Let’s take a look at a bowling ball and a golf ball. Gravity
puts more force on the bowling ball than on the golf ball. So the bowling ball should accelerate faster
since there’s more force on it. However, the bowling ball is heavier so it is harder to get it moving. Vice
versa, the golf ball has less force pulling on it but it’s easier to get moving. Do you see it? The force and
inertia thing equal out so that all things accelerate due to gravity at the same rate of speed.
Gravity had to be one of the first scientific discoveries. Whoever the first guy was to drop a rock on his
foot, probably realized that things fall down! However, even though we have known about gravity for
many years, it still remains one of the most elusive mysteries of science. At this point, nobody knows
what makes things move toward a body of mass.
Why did the rock drop toward the Earth and on that guy’s foot? We still don’t know. We know that it
does, but we don’t know what causes a gravitational attraction between objects. Gravity is also a very
weak force. Compared to magnetic forces and electrostatic forces, the gravitational force is extremely
weak. How come? No one knows. A large amount of amazing brain power is being used to discover these
mysteries of gravity. Maybe it will be you who figures this out!
Exercises
1. Of the following objects, which ones are attracted to one another by gravity? a) Apple and Banana b) Beagle and Chihuahua c) Earth and You d) All of the above
2. True or False: Gravity accelerates all things differently.
3. True or False: Gravity pulls on all things differently.
4. If I drop a golf ball and a golf cart at the same time from the same height, which hits the ground first?
5. There is a monkey hanging on the branch of a tree. A wildlife biologist wants to shoot a
tranquilizer dart at the monkey to mark and study him. The biologist very carefully aims directly
at the shoulder of the monkey and fires. However, the gun makes a loud enough noise that the
monkey gets scared, lets go of the branch and falls directly downward. Does the dart hit where
the biologist was aiming, or does it go higher or lower then he aimed? (This, by the way, is an old
thought problem.)
Answers to Exercises: Watch Your Weight
1. Of the following objects, which ones are attracted to one another by gravity?
a) Apple and Banana b) Beagle and Chihuahua c) Earth and You d) All of the above
2. True or False: Gravity accelerates all things differently (Gravity accelerates all things equally, which means all things speed up the same amount as they fall)
3. True or False: Gravity pulls on all things differently (Gravity does pull on things differently. It pulls greater on objects that weigh more, and weight is a measure of how much gravity is pulling on an object.)
4. If I drop a golf ball and a golf cart at the same time from the same height, which hits the ground first? (They both hit the ground at the same time.)
5. There is a monkey hanging on the branch of a tree. A wildlife biologist wants to shoot a tranquilizer
dart at the monkey to mark and study him. The biologist very carefully aims directly at the shoulder of
the monkey and fires. However, the gun makes a loud enough noise that the monkey gets scared, lets go
of the branch and falls directly downward. Does the dart hit where the biologist was aiming or does it go
higher or lower then he aimed? (The monkey and the dart fall downward at the same rate of speed. So
the dart would hit exactly where the biologist aimed! In fact, if the monkey didn’t let go, the dart would
have hit lower than the biologist aimed.)
FORCE AND MASS UNITS
Units In the US system of units, both mass and weight are measured in “pounds” or “lb”. That’s a BIG problem, because mass isn’t the same as weight, so how could their units be the same? The answer is, the units are not the same, but they look very similar. The units for mass are kg (kilograms) or lbm (pronounced “pounds mass”) and the units for force are N (Newtons) or lbf (pronounced “pounds force”). The trouble comes in when we drop that third character and “lbf” or “lbm” becomes just plain “lb”. That’s the problem, and it’s a major headache for students to understand. Here’s the main thing I want you to remember: 1 lbm is NOT equal to 1 lbf.
FRICTION
Friction is the force between two objects in contact with one another when one object moves (or tries to move) across another on the surface. Friction is dependent on the types materials that are in contact with one another (rubber versus leather, for example), and how much pressure is put on the materials, and whether the surfaces are wet, dry, hot, cold… it’s really complicated. Friction happens due to the electromagnetic forces between two objects. Friction is not necessarily due to the roughness of the objects but rather to chemical bonds “sticking and slipping” over one another.
TYPES OF FRICTION
There are two main types of friction: static and kinetic. Static friction is the friction between two objects that
are not moving. Kinetic (or sliding) friction is the friction between two objects where at least one of them is
moving. If you push a box across the floor, the floor resists the motion of the box by exerting a friction force on
the box. If the box is sliding across the floor, it’s kinetic friction. If you’re pushing but the box hasn’t moved
yet, it’s static friction. A car sliding sideways off the road is experiencing kinetic friction between the rubber
tires and the pavement.
Here’s a cool experiment that will show you how to reduce the friction using a balloon and an old CD by lifting
up the CD on a cushion of air, like an air hockey puck
STATIC AND KINETIC FRICTION
What if there’s a lot of friction? Have you ever felt that you need to give something a shove before it starts moving? You have to overcome static friction in order to experience kinetic friction. (Static friction is higher in magnitude than kinetic friction, generally speaking.) The equation for determining the friction is: f = μ Fnormal, where μ = the coefficient of friction. For kinetic friction: fkinetic = μk Fnormal, where μk = the coefficient of kinetic friction For static friction: fstatic = μs Fnormal, where μs = the coefficient of kinetic friction Scientists have to figure out μs and μk by doing experiments, and they compile that data in tables for others to look up when they need it.
EVERYDAY FRICTION
Here’s a neat way to measure the friction that use everyday when you walk around in your shoes.
Recap for Forces:
A force is a push or a pull.
There are four fundamental forces. In order of strength they are strong nuclear force, electromagnetism,
weak nuclear force, and gravity.
A force field is an invisible area around an object within which that object can cause other objects to
move.
A force field can be attractive (pull an object towards it) or repulsive (push an object away).
The closer something gets to the object causing the force, the stronger the force gets on that object. This
is the inverse-square law.
The four basic force fields are gravity, magnetic, electric, and electromagnetic.
There are two main categories for forces: action-at-a-distance and contact forces.
An object will be pushed or pulled in the direction in which the overall net force is acting on it.
The net force is the sum of all the forces on an object.
Tracking Treads
Overview: Now let’s talk about the other ever-present force on this Earth, and that’s friction. Friction is
the force between one object rubbing against another object. Friction is what makes things slow down.
Without friction things would just keep moving unless they hit something else. Without friction, you
would not be able to walk. Your feet would have nothing to push against and they would just slide
backward all the time like you’re doing the moon walk.
What to Learn: Today you get to discover how friction is a complicated interaction between pressure and the type of materials that are touching one another.
Materials
shoes (about 5 different ones)
board, or a tray, or a large book at least 15 inches long and no more than 2 feet long.
ruler or yardstick
protractor
pencil
partner
Lab Time
1. Put the board (or whatever you’re using) on the table.
2. Put the shoe on the board with the back of the shoe touching the back of the board.
3. Have a partner hold the ruler upright (so that the12-inch end is up and the 1-inch end is on the table) at the back of the board.
4. Slowly lift the back of the board, leaving the front of the board on the table. (You’re making a ramp with the board). Eventually the shoe will begin to slide.
5. Stop moving the board when the shoe slides and measure the height that the back of the board was lifted to.
6. Test each shoe three times to verify your data.
7. Look at the 5 shoes you chose and test them. Before you do, make a hypothesis for which shoe will have the most friction.
8. On a scale from 1 to 5 (or however many shoes you’re using) rate the shoes you picked. 1 is low friction and
5 would be high friction. Write the hypothesis next to a description of the shoes on a piece of paper. The greater the friction the higher the ramp has to be lifted. Test all of the shoes.
9. Analyze the shoes. Do the shoes with the most friction show any similarities? Are the bottoms made out of the same type of material? What about the shoes with very little friction?
Tracking Threads Data Table
Item/Object Description Guess First! Rank each: 1 for Height of Board when
lowest friction, 5 for most friction. Shoe Starts to Slide
Reading
Since friction is all about two things rubbing together, the more surface that’s rubbing, the more friction you get. Ever notice how the tire on a car has treads, but a race car tire will be absolutely flat with no treads at all?
The race car doesn’t have to worry about rain or stuff on the road, so it gets every single bit of the tire
to be touching the surface of the track. That way, there is as much friction as possible between the tire
and the track. The tire on your car has treads to cut through mud and water to get to the nice firm
road underneath. The treads actually give you less friction on a flat, dry road.
You can opt to use a skateboard shoe for this experiment. Notice that a skateboard shoe has very a
flat bottom compared to most other shoes. This is because a skateboarder wants as much of his or her
shoe to touch the board at all times, having as much contact friction as possible.
Exercises Answer the questions below:
1. What is friction?
2. What is static friction?
3. What is kinetic friction?
Answers to Exercises: Tracking Treads
4. What is friction? (the resistance that happens when two surfaces come into contact with each other)
5. What is static friction? (the resistance that must be overcome for an object to move )
6. What is kinetic friction? (the resistance that occurs when the objects are in motion, but still in contact)
NEWTON’S SECOND LAW OF MOTION
To review, Newton’s First Law deals with objects that have balanced forces on it and predicts how they will behave. It’s sometimes called the law of inertia, and it’s the law that is responsible for helping you figure out which egg is raw or hard-boiled without having to crack it open. (If you haven’t done this, you really need to. All you have to do is set the egg spinning on the counter, then gently touch the top with a finger for a second, then release. The egg that stops dead is hard-boiled, and the one that starts spinning again in raw. Don’t know why this works? The raw egg has a liquid center that isn’t connected to the hard shell. When you stopped the shell for a split second, the innards didn’t have time to stop, and they have inertia. When you removed your finger, the liquid exerts a force on the shell and starts it spinning again. The hard-boiled egg is solid all the way through, so when you stopped the shell, the whole thing stops. Newton’s First Law in action.) Newton’s Second Law of Motion deals with the behavior of objects that have unbalanced forces. The acceleration of an object depends on two things: mass and the net force actin on the object. As the mass of an object increases, like going from a marshmallow to a bowling ball, the acceleration decreases. Or a rocket burning through its fuel loses mass, so it accelerates and goes faster as time progresses. There’s a math equation for the second law, and it’s stated like this: F = ma, where F is the net force, m is the mass, and a is the acceleration. It’s important to note that Fis the vector sum of all forces applied to the object. If you miss one or double count one of them, you’re in trouble. Also note that F is the external forces exerted on the object by other objects, not the internal forces because those cancel each other out.
NEWTON’S SECOND LAW WITH VECTOR ADDITION
Newton’s laws help us figure out how objects will behave when we apply forces that cause it to move. This is useful in order to be able to to land rockets on the moon, designing race cars that will accelerate faster around a turn on the highway, and so much more. But there’s a problem… A lot of people can easily recite Newton’s laws, but they either can’t use them or understand how to apply them to the real world because they don’t really know what they mean. There’s evidence all around us about how the world works, but depending on what you focus on, you’re going to stack different examples to support your beliefs about how the world works.
I can’t tell you how many times students ask me how they can make a real light saber from Star Wars. They want to know how to make a light beam into a solid object that’s tougher than steel. While I’ve never seen light do this in the real world, this is one of those unfortunate cases where too much media (like video games and movies) gets mixed in with how we see the world, and warps our understanding of the physical principles of the universe. There are thousands of movies and video games that use “cartoon physics” to get an action to appear on the screen a certain way, and when you watch that, it forms as a model in your mind about how the world works. If you’ve ever seen characters suspended in mid-air until they realize there’s no ground beneath them and then they fall, or people plunging through solid walls at high speeds leaving an exact trace of their outline as they pass through it, or scaring someone which causes them to jump abnormally high in the air, you’ve seen this in action. Now don’t get me wrong – I love a good movie just as much as the next person, but when you’re spending more time watching the world through a box, you’re going to make a different model in your mind about how things behave than if you were spending time in the real world. It’s not just media, though. One of the most common misconceptions we’ve already busted in a previous lesson is how an object needs a continuous force on it in order to continue it’s motion. This one is totally not true – it’s the absence of forces that makes continue its motion. One of the tasks of this physics course is to unravel these misconceptions and help you understand what’s really going on by having you think for yourself, figure out what’s going on, and evaluate your own thinking to see if it really makes sense. When a body moves through a fluid like air or water, the drag force is going to come into your equations. Some examples include a cannon ball sinking into the ocean, a jet ski zipping along on a lake, a truck on the highway, a bird flying through the air, or a parachutist falling to earth. Even a particle of dust has been found to encounter so much air resistance that it can take an hour to fall a single foot of distance. Objects in free fall mean that the drag force is equal to the weight of the object: Fd = mg. So far, we’ve looked at single objects being tossed, thrown, flung, and dropped. But what happens if two objects are connected together, like the space shuttle on a rocket or a truck hauling a boat?
VECTOR SUMS
How do you find the vector sum of all the forces acting on an object? We already looked at how to use a FBD to calculate the net applied force on an object, so now let’s put it together with our knowledge about gravity (Fgrav = mg) and friction (Ffriction = μ fnormal) by using our equation: Fnet = ma.
AIR RESISTANCE
When we studied Free Fall Motion, we assumed that all objects fall with the same acceleration of G or 9.81 m/s2 . Well, that wasn’t the whole truth, because not all objects fall with the same acceleration. But it’s a good place to start out when we’re getting our feet wet with physics. (You’ll find this happens a lot when you get to more advanced concepts… you learn the easier stuff first by ignoring a lot of other things until you can learn how to incorporate more things into your equations.) So why do objects stop accelerating and reach terminal velocity, and how why do more massive objects fall faster than less massive? To answer this, we’ll take a look at air resistance and Newton’s Second Law using the F = ma equation.
DRAG FORCE
When an object falls through the air, it runs into air resistance. How much air resistance depends on the size
and shape of the object in addition to how fast it’s falling. It’s calculated in engineering fluid mechanics
courses as the drag force, but for now, let’s keep it simple and know that the faster an object’s speed and the
larger cross-section it has, the more air resistance it encounters. A ping pong ball and a golf ball have the same
cross section, so you’d expect them to hit the ground at the same time, even though the ping pong ball weighs
20 times less than the golf ball (2.7 grams versus 46 grams). A golf ball and a tennis ball are about 50 grams
each, but the tennis ball is nearly twice the diameter, so you’d expect the tennis ball to hit more air resistance
than the golf ball.
Think about it this way: If you take two sheets of paper and crumple only one of them up, and drop them from
the same height, which one hits the ground first? The crumpled one, because it encountered less air resistance
on the way down. If you drop the golf ball from a helicopter way up in the sky, the ball will accelerate and pick
up speed, which means it’s also picking up more air resistance, until it reaches a point where it’s stops
accelerating (called its terminal velocity), which is the balance point between the drag force and the weight of
the object.
This is the point where the net force is zero, since it’s no longer accelerating. Would you expect a bowling ball
and a basket ball the same size to hit the ground at the same time if dropped from our helicopter? Not if you
take into account air resistance! The only place where you’re not going to run into this drag force is where
there’s little or no air… like on the moon.
When a body moves through a fluid like air or water, the drag force is going to come into your equations. Some
examples include a cannon ball sinking into the ocean, a jet ski zipping along on a lake, a truck on the highway,
a bird flying through the air, or a parachutist falling to earth. Even a particle of dust has been found to
encounter so much air resistance that it can take an hour to fall a single foot of distance. Objects in free fall
mean that the drag force is equal to the weight of the object: Fd = mg.
So far, we’ve looked at single objects being tossed, thrown, flung, and dropped. But what happens if two
objects are connected together, like the space shuttle on a rocket or a truck hauling a boat?
Weighty Issue
Overview: If I drop a ping pong ball and a golf ball from the same height, which one hits the ground first? Howabout a bowling ball and a marble?
What to Learn: Students will learn that gravity accelerates all things equally. Objects near the Earth fall to theground unless something holds them up.
Materials (per lab group)
ping pong ball
golf ball
feather
balloon
bouncy ball
eraser
pencil
2 sheets of paper (crumple one up to the size of a golf ball)
paperclip
empty water bottle
Lab Time
1. Take a careful look at both objects and make a prediction about which object will hit the ground first if they are dropped from the same height. Record your hypothesis.
2. Test your prediction. Hold both objects at the same height. Make sure the bottom of both objects is the same distance from the floor.
3. Let them go as close to the same time as possible. Sometimes it’s helpful to roll them off a book.
4. Watch carefully. Which hits the ground first, the heavier one or the lighter one?
5. Try it three times and watch carefully. It will be a little easier for the person who isn’t dropping them to see what happens.
Weighty Issue Data Table 1
Item/Object Item/Object Guess First: Record Observation:
A B Which one will hit first? Which one hit first?
Weighty Issue Data Table 2
To determine the mass in kg, use the following conversion: 1 pound = 0.4536 kg.
For calculating area of a 3D object, use the side that the oncoming air sees as it falls to the ground.
For a ball, it’s Asphere = ( r2) / 4. For a sheet of paper, it’s (length) x (width). Don’t forget to write your units!
Object A Mass A Area A Object B Mass B Area B Which hit first?
Reading
For this experiment, you’ll need two objects of different weights: a marble and a golf ball, or a tennis ball and a penny for example. You’ll also need a sharp eye and a partner.
When dropped from the same distance, you should see that both objects hit the ground at the same
time! Gravity accelerates both items equally and they hit the ground at the same time. Any two objects
will do this, a brick and a Buick, a flower and a fish, a kumquat and a cow!
“But,” I hear you saying, “If I drop a feather and a flounder, the flounder will hit first every time!” OK, you got me there. There is one thing that will change the results and that is air resistance.
The bigger, lighter and fluffier something is, the more air resistance can affect it and so it will fall more
slowly. Air resistance is a type of friction which we will be talking about later. In fact, if you removed air
resistance, a feather and a flounder would hit the ground at the same time!
Where can you remove air resistance? The moon! One of the Apollo missions actually did this (well, they
didn’t use a flounder, they used a hammer). An astronaut dropped a feather and a hammer at the same
time and indeed, both fell at the same rate of speed and hit the surface of the moon at the same time.
Ask someone this question: Which will hit the ground first, if dropped from the same height, a
bowling ball or a tennis ball? Most will say the bowling ball. In fact, if you asked yourself that
question 5 minutes ago, would you have gotten it right? It’s conventional wisdom to think that the
all things equally. In other words, gravity makes all things speed up or slow down at the same rate.
This is a great example of why the scientific method is such a cool thing. Many, many years ago, there
was a man of great knowledge and wisdom named Aristotle. Most people believed whatever he said to
be true. The trouble was he didn’t test everything that he said. One of his statements was that objects
with greater weight fall faster than objects with less weight. Everyone believed that this was true.
Hundreds of years later, Galileo came along and said, “Ya know…that doesn’t seem to work that way.
I’m going to test it.” The story goes that Galileo grabbed a melon and an orange and went to the top of
the Leaning Tower of Pisa. He said, “Look out below!” and dropped them! By doing that, he showed
that objects fall at the same rate of speed no matter what their size.
It is true that it was Galileo who “proved” that gravity accelerates all things equally no matter what their weight, but there is no real evidence that he actually used the Leaning Tower of Pisa to do it.
Exercises Answer the questions below:
1. What did you notice from your data? Did heavier or lighter objects fall faster? Did more massive objects or smaller objects fall faster? What characteristic seemed to matter the most?
2. Is gravity a two-way force, like the attractive-repulsive forces of a magnet?
3. If I were to drop a bowling ball and a balloon filled with a gas six times heavier than air (sulfur
hexafluoride SF6) and inflated to the exact size of the bowling ball from my roof, which will strike
the ground first?
Answers to Exercises: Weighty Issue
1. What did you notice from your data? Did heavier or lighter objects fall faster? Did more massive objects or smaller objects fall faster? What characteristic seemed to matter the most? (see data tables)
2. Is gravity a two-way force, like the attractive-repulsive forces of a magnet? (No, only attractive.)
3. If I were to drop a bowling ball and a balloon filled with a gas six times heavier than air (sulfur
hexafluoride SF6) and inflated to the exact size of the bowling ball from my roof, which will strike
the ground first? (Both, unless it’s windy!)
TWO-BODY PROBLEMS
There are situations where you have two objects interacting with each other, which means that you’ll have two unknown variables you’ll solve for (usually acceleration). You can solve these types of problems in a couple different ways. First, you can look at the entire system and consider both objects as only one object. For example, the Earth and Moon might be combined into one object if we’re looking at objects that orbit the sun, so the mass of the Earth and Moon would be combined into a single mass, m, and would also have the same acceleration, a. This approach is used if you really don’t care about what’s going on between the two objects. Or you could treat each object as it’s own separate body and draw FBD for each one. This second approach is usually used if you need to know the forces acting between the two objects.
NEWTON’S THIRD LAW OF MOTION
Newton’s Third and final law of motion is that every action has an equal and opposite reaction. Even though
this is the most well-known of Newton’s Three, it seems to me to be the hardest to fully comprehend. Again, it
is a tribute to Newton that he was able to see this law. For every action, every force, the same action/force
happens in the opposite direction. As you sit on your chair reading this, gravity is pulling down with a certain
force (the force of your weight and the weight of the chair). The floor is pushing up with the same force.
Newton was able to see that when two (or more) objects interact with each other, they exert forces on each
other.
Balloon Racers
Overview: We’re going to experiment with Newton’s ThirdLaw by blowing up balloons and letting them
rocket,race, and zoom all over the place. When you first blow up a balloon, you’re pressurizing the inside
of the balloon by adding more air from your lungs into the balloon. Because the balloon is made of
stretchy rubber, like a rubber band, it wants to snap back into the smallest shape possible as soon as it
gets the chance, which usually happens when the air escapes through the nozzle area. When this
happens, the air inside the balloon flows in one direction while the balloon zips off in the other.
What to Learn: The motion of objects can be observed and measured.
Materials
balloons
string
wood skewer
two straws
caps (4, like the tops of milk jugs, film canisters, or anything else round and plastic about the size of a quarter)
wooden clothespin
stiff cardboard (or four popsicle sticks)
hot glue gun
meter or yardstick
stopwatch Lab Time
1. Blow up the balloon (don’t tie it), then let it go. Wheee! Okay, so that step was to get the balloon ready for the experiment. Now…
2. Tie one end of the string to a chair.
3. Blow up the balloon (don’t tie it).
4. Tape a straw to it so that one end of the straw is at the front of the balloon and the other is at the nozzle of the balloon.
5. Thread the string through the straw and pull the string tight across your room.
6. Let go. With a little bit of work (unless you got it the first time) you should be able to get the balloon to shoot about ten feet along the string.
Balloon Racer Data Table
Trial Number of Breaths How Far Did It Go? How Long Did It Take?
to Blow Up Balloon (measure in feet or meters) (measure in seconds)
Reading
When you first blow up a balloon, you’re pressurizing the inside of the balloon by
adding more air from your lungs into the balloon. Because the balloon is made of
stretchy rubber, like a rubber band, it wants to snap back into the smallest shape
possible as soon as it gets the chance, which usually happens when the air escapes
through the nozzle area. When this happens, the air inside the balloon flows in one
direction while the balloon zips off in the other.
Have you ever noticed how the balloon crazily zips all over the place when you let go? Why is that?
The balloon zigzags all over because of something called ”thrust vectoring,” which means the direction of the balloon changes depending on the angle that the nozzle makes at the end (the part you blew into).
Think of a fire hose. There’s a lot of water rushing out of the end of a fire hose, right? A fire hose not only has high-speed water rushing out, but there’s also a lot of volume in a fire hose. How easy do you think it would be to try to change the direction of all that water? You’d actually feel a “kick” back from the water when you tried to angle around a fire hose operating at full blast. That “kick” is the same reaction force that propels both balloons and fighter aircraft into their aerobatic tricks.
Newton’s Third Law of Motion states that for every action, there is an equal and opposite reaction. These experiments are a great demonstration of Newton’s Third Law. The air inside the balloon shoots off in one direction, and the balloon itself rockets in the opposite direction.
It’s also a good opportunity to bring up some science history. Many folks used to believe
that it would be impossible for something to go to the moon, because once something
got into space there would be no air for the rocket engine to push against and so the
rocket could not “push” itself forward.
In other words, those folks would have said that a balloon shoots along the string because
the air coming out of the balloon pushes against the air in the room. The balloon gets
pushed forward. You now know that that’s silly! What makes the balloon move forward is
the mere action of the air moving backward. Every action has an equal and opposite
reaction.
Exercises Answer the questions below:
1. What is Newton’s Third Law of Motion? 2. Why does the balloon stop along the string?
Answers to Exercises: Balloon Racers
1. What is Newton’s Third Law of Motion? (For every action, there is an equal and opposite reaction.)
2. Why does the balloon stop along the string? (Friction between the string and straw.)
THIRD LAW EXPLAINED
This law helps you walk. As you walk, you push backwards against the ground. The ground
gives an equal and opposite push to you so you move forward. Try to imagine someone walking
in a canoe. (I don’t recommend trying this, unless you know how to swim and are willing to get
wet!) As the person steps forward, the canoe moves backward. The equal and opposite force of
the walking moves the person forward just as far as it moves the canoe backward.
INERTIA AND THE SECOND AND THIRD LAW
Suppose you are thinking… “But how come as I walk on my floor, my house doesn’t move
backwards like the canoe?” Then I would say… Ahhh, good, I’m glad you’re paying attention!
Let’s go back to Newton’s Second Law again. Force equals mass times acceleration. What is the
mass of you compared to your house? Pretty small right? So the force you create to move your
mass forward, is nowhere near the force that is required to move the house backward (especially
since your house is anchored to the earth.) You do push backward on your house but due to the
immense inertia of the house it doesn’t move.
FORCES COME IN PAIRS
The basic idea I want you to remember about Newton’s Third Law is that forces come in pairs. The wheels on a car spin, and as they do they grip the road and push the road back while at the same time the road pushes forwards on the wheel.
Review for Forces and Newton’s Three Laws of Motion:
1. Newton’s First Law is an object at rest tends to stay at rest and an object in motion tends to stay in motion unless a force acts against it.
2. Inertia is a quality of an object that determines how difficult it is to get that object to move, to stop moving or to change directions.
3. Force is a push or a pull on something. 4. Newton’s Second Law is F=ma or Force equals mass x acceleration. In other words,
the more mass something has and/or the faster it’s accelerating, the more force it will put on whatever it hits.
5. The more mass something has, the more force that’s needed to get it to accelerate. a=F/m
6. Things accelerate because there is a net force acting upon them. 7. Things stop accelerating (maintain a constant velocity) because the forces acting on
them have equaled out. 8. Newton’s Third Law states that every action has an equal and opposite reaction.
APPLYING NEWTON’S LAWS
The best way to learn how to solve physics problems is to solve physics problems. You can’t just read about it and think about it in your head… you actually have to do it, just like riding a bike. You can read all about bicycles, how they work and what the individual parts do, but until you sit in the seat and try to ride the thing, it’s really hard to understand. I am going to do a series of different sample physics problems in the videos below and explain everything in detail so you can really see how to apply Newton’s Laws of Motion to problems in the real world. After you’re done watching the samples, download your practice problem set (at the end of the lessons) and try it yourself!
SLED PROBLEM
Sleds are great to practice physics problems with, because there’s no friction associated with the problem (it’s sitting on ice, not on the ground). This is a good one to start with to get used to how we use the kinematic equations along with Newton’s laws and FBD’s to solve real problems.
REFERENCE FRAMES AND THE TRUCK PROBLEM
This is a really common thing to see happen in the real world, and one that people have a hard time seeing from the point of view of an outside observer just sitting on the side of the road. If you’ve ever been in a truck where this happened to you, now you know why.
RUBBER TIRE PROBLEM
Here’s a good example of how non-moving objects can be analyzed for missing components by setting the acceleration term in Newton’s second law to zero. (Although I’ve never tried this one, I can only imagine that in the real world, the tire would actually be moving.)
USING NEWTON’S LAWS TOGETHER
This is a good example of Newton’s second and third laws in action and how to use both laws to help you solve a problem…
CHANDELIER PROBLEM
Imagine this one is a chandelier hanging from the ceiling, and you want to find out if your cables are strong enough…
BREAKING LOOSE
This is a great example of how to calculate forces for a static (no motion) system, and then what happens if you break loose and allow motion to happen. Note how the coordinate system was oriented to make the math a lot easier.
PULLEY PROBLEM
Pulley problems are common in physics, and in this example you will learn how to draw FBD with different coordinate systems that work with each drawing individually.
HOW TO GAIN AND LOSE WEIGHT
You can gain and lose weight just by standing on your bathroom scale in an accelerating elevator. In this problem, we’ll look at what happens if there’s constant velocity, positive and negative acceleration, and also free fall motion (yikes!).
HOMEWORK PROBLEMS WITH SOLUTIONS
On the following pages is the homework assignment for this unit. When you’ve completed all the videos from this unit, turn to the next page for the homework assignment. Do your best to work through as many problems as you can. When you finish, grade your own assignment so you can see how much you’ve learned and feel confident and proud of your achievement! If there are any holes in your understanding, go back and watch the videos again to make sure you’re comfortable with the content before moving onto the next unit. Don’t worry too much about mistakes at this point. Just work through the problems again and be totally amazed at how much you’re learning. If you’re scoring or keeping a grade-type of record for homework assignments, here’s my personal philosophy on using such a scoring mechanism for a course like this: It’s more advantageous to assign a “pass” or “incomplete” score to yourself when scoring your homework assignment instead of a grade or “percent correct” score (like a 85%, or B) simply because students learn faster and more effectively when they build on their successes instead of focusing on their failures. While working through the course, ask a friend or parent to point to three questions you solved correctly and ask you why or how you solved it. Any problems you didn’t solve correctly simply mean that you’ll need to go back and work on them until you feel confident you could handle them when they pop up again in the future.
10. An F-14 Tomcat weighs 30 tons with all ordinance attached and fully fueled. The pilot knows that his plane
needs a speed of 325 ft/s to take off. The engine for the Tomcat only produces 27,000 pounds of thrust and
the runway for the aircraft carrier is only 320 feet long. What force must the catapult of the aircraft carrier
apply to the pilot’s airplane so that he can takeoff safely? (Assume both the engine and the catapult exert a
constant force over the 325 ft runway)
Quick Notes Page 8
Quick Notes Page 9
Quick Notes Page 10
Quick Notes Page 11
Quick Notes Page 12
Quick Notes Page 13
pm �� �
nm �� �
em �� �
c � �
e �� �
k pe� � � �
G �� � �
g �
�
W
�
�
� m�
�
q � � � � � � �
q
q
q �
MECHANICS ELECTRICITY
0x x xa tà � �
20 0
12xx x t a� � � xt
�2 20 2x x xa x xà � � � 0
netFFa
m� ��
m
��
fF m� nF� �
2
ca �r
p mv�� �
p F tD D�� �
212
K mv�
cosE W F d Fd qD � � ��
EPt
DD
�
20 0
12
tq q w a� � � t
0 tw w a� �
� cos 2x A ftp�
net
I Itt
a � �� ��
sinr F rFt �� � q
L Iw�
L ttD � D
212
K Iw�
sF k x�� �
2
2sU kx� 1
mV
r �
a = acceleration A = amplitude d = distance E = energy f = frequency F = force I = rotational inertia K = kinetic energy k = spring constant L = angular momentum � = lengthm = mass P = power p = momentum r = radius or separation T = period t = time U = potential energy V = volume v = speed W = work done on a system x = position y = height a = angular acceleration
m = coefficient of friction q = angle r = density t = torque w = angular speed
gU mg yD � D
2Tf
pw
� � 1
2smTk
p�
2pTg
p� �
1 22g
m mF G
r�
�
gFg
m��
�
1 2G
Gm mU
r� �
1 22E
q qF k
r�
�
qI
tDD
�
RAr� �
VIRD�
P I VD�
si
R R� i
1 1
p iiR R
�
A = area F = force I = current � = lengthP = power q = charge R = resistance r = separation t = time V = electric potential r = resistivity
WAVES
vf
l � f = frequency v = speed l = wavelength
GEOMETRY AND TRIGONOMETRY
Rectangle A bh�
Triangle 12
A bh�
Circle 2A p�
2C p�r
r
Rectangular solid V wh� �
Cylinder
V rp� �2
2 2S r rp p� �� 2
Sphere 3
3V rp� 4
24S rp�
A = area C = circumference V = volume S = surface area b = base h = height � = lengthw = width r = radius
Right triangle
2 2 2c a b� �
sin ac
q �
cos bc
q �
tan ab
q �
c a
b90�q
CONSTANTS AND CONVERSION FACTORS
Proton mass, 271.67 10 kgpm �� �
Neutron mass, 271.67 10 kgnm �� �
Electron mass, 319.11 10 kgem �� �
Avogadro’s number, 23 -10 6.02 10 molN � �
Universal gas constant, 8.31 J (mol K)R � �
Boltzmann’s constant, 231.38 10 J KBk �� �
Electron charge magnitude, 191.60 10 Ce �� �
1 electron volt, 191 eV 1.60 10 J�� �Speed of light, 83.00 10 m sc � �
Universal gravitational constant,
11 3 26.67 10 m kg sG �� � �
Acceleration due to gravityat Earth’s surface,
29.8 m sg �
1 unified atomic mass unit, 27 21 u 1.66 10 kg 931 MeV c�� � �� Planck’s constant, 34 156.63 10 J s 4.14 10 eV sh �� � � ��
25 31.99 10 J m 1.24 10 eV nmhc �� � � ��
Vacuum permittivity, 12 2 20 8.85 10 C N me �� � �
Coulomb’s law constant, 9 201 4 9.0 10 N m Ck pe� � � �
AVacuum permeability, 70 4 10 (T m)m p �� � �
Magnetic constant, 70 4 1 10 (T m)k m p �� � � �
5 1 atmosphere pressure, 5 21 atm 1.0 10 N m 1.0 10 Pa� � � �
UNIT SYMBOLS
meter, m kilogram, kgsecond, sampere, Akelvin, K
mole, mol hertz, Hz
newton, Npascal, Pajoule, J
watt, W coulomb, C
volt, Vohm,
henry, H
farad, F tesla, T
degree Celsius, C� W electron volt, eV
2
A
�
�
PREFIXES Factor Prefix Symbol
1012 tera T
109 giga G
106 mega M
103 kilo k
10�2 centi c
10�3 milli m
10�6 micro m
10�9 nano n
10�12 pico p
VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES
q �0
�30
�37 45� �
53 60� 90�
sinq 0 1 2 3 5 2 2 4 5 3 2 1
cosq 1 3 2 4 5 2 2 3 5 1 2 0
tanq 0 3 3 3 4 1 4 3 3 �
The following conventions are used in this exam. I. The frame of reference of any problem is assumed to be inertial unless
otherwise stated. II. In all situations, positive work is defined as work done on a system.
III. The direction of current is conventional current: the direction in whichpositive charge would drift.
IV. Assume all batteries and meters are ideal unless otherwise stated.V. Assume edge effects for the electric field of a parallel plate capacitor
unless otherwise stated.
VI. For any isolated electrically charged object, the electric potential isdefined as zero at infinite distance from the charged object.
MECHANICS ELECTRICITY AND MAGNETISM
0x x xa tà � �
x x� � 20 0Ãx t � a t
21
x
�2 20 2x x xa x xà � � � 0
netFFa
m m� ��
��
f nF Fm�� �
2
car�
p mv�� �
p F tD D���
212
K mv�
cosE W F d Fd qD � � ��
EPt
DD
�
20 0
12
t tq q w a� � �
0 tw w a� �
� � cos cos 2x A t A fw� � tp
i icm
i
m xx
m�
net
I Itt
a � �� ��
sinr F rFt �� � q
L Iw�
L ttD D�
212
K Iw�
sF k x� ��
a = acceleration A = amplitude d = distance E = energy F = force f = frequency I = rotational inertia K = kinetic energy k = spring constant L = angular momentum � = lengthm = mass P = power p = momentum r = radius or separation T = period t = time U = potential energy v = speed W = work done on a system x = position y = height a = angular acceleration m = coefficient of friction q = angle t = torque w = angular speed
212sU kx�
gU mg yD D�
2 1Tf
pw
� �
2smTk
p�
2pTg
p� �
1 22g
m mF G
r�
�
gFg
m��
�
1 2G
Gm mU
r� �
1 22
0
14E
q qF
rpe�
�
EFE
q�
� �
20
14
qE
rpe�
�
EU q VD D�
0
14
qV
rpe�
VEr
DD
��
QV
CD �
0ACd
ke�
0
QE
Ae�
� 21 12 2CU Q V CD� � VD
QI
tDD
�
RAr� �
P I VD�
VIRD�
si
R R� i
1 1
p iiR R
�
pi
C C� i
1
s iC
� 1
iC
0
2IBr
mp
�
A = area B = magnetic field C = capacitance d = distance E = electric field e = emfF = force I = current � = lengthP = power Q = charge q = point charge R = resistance r = separation t = time U = potential (stored)
energy V = electric potential v = speed k = dielectric constant r = resistivity
q = angle F = flux
MF qv B� �� �
�
sinMF qv q�� �
B
MF I B� ����
�
sinMF I Bq����
�
B B AF � � ��
cosB B AqF ���
B
te DF
D� �
B ve � �
�
FLUID MECHANICS AND THERMAL PHYSICS
A = areaF = force h = depth k = thermal conductivity K = kinetic energy L = thickness m = mass n = number of moles N = number of molecules P = pressure Q = energy transferred to a
system by heating T = temperature t = time U = internal energy V = volume v = speed W = work done on a system y = height�r = density
mV
r �
FPA
�
0P P gr� � �h
bF Vgr�
1 1 2 2A v A v�
21 1
12
P gy vr� �
22 2
12
P gy vr r� � �
1r
2
kA TQt L
DD
�
BPV nRT Nk T� �
32 BK k� T
VW PD� �
U Q WD � �
MODERN PHYSICS
E = energy f = frequency K = kinetic energy � = mass p = momentum l = wavelength f = work function�
E hf�
maxK hf f� �
hp
l �
2E mc�
WAVES AND OPTICS
d = separation f = frequency or
focal lengthh = height L = distance M = magnification m = an integer n = index of
refraction s = distance � = speed l = wavelength q = angle�
vf
l �
cnÃ
�
1 1 2sin sinn nq � 2q
1 1
i os s f� � 1
i
o
hM
h� � i
o
ss
L mlD �sind mq l�
GEOMETRY AND TRIGONOMETRY
A = area C = circumference V = volume S = surface area b = base h = height � = length w = width r = radius
