Post on 04-Jul-2020
transcript
How can we distinguish between energy, force and motion?
Big Ideas:
How are energy, force and motion related?
What role do energy and force play in motion?
falling rhino
falling rhino slip and slide
Consider the energy of, and forces on, falling objects:
physics of falling
What is the cause of motion?
Do forces always involve two objects?
Do forces always require contact?
Can forces involve more than 2 objects?
More simply: a force is an interaction between 2 (or more objects) that influences the motion between the objects.
In physics, a force is any influence that
causes an object to undergo a change in
speed, a change in direction, or a change
in shape.
In other words, a force is that which can cause an object
with mass to change its velocity, i.e., to accelerate, or
which can cause a flexible object to deform.
A Push Or
Pull
What is a force?
Recognizing forces and motion interactions
Which of the following are generally true of force and motion?
♦ come up with a confirming example – where it is true
♦ can you find at least one single example that shows it false?
• A net force it will speed up.
• A net force in the same direction it is moving it will
speed up.
• An increasing net force it will speed up.
• A net force in a direction opposite its motion it will
slow down.
• A decreasing net force it will slow down.
• No net force it must be at rest.
• No net force it will slow down.
• No net force it will continue moving at constant speed
(or remain stationary).
A force represents the interaction of an object
(system) with its environment (the forces exerted
on the system) by an agent (the cause of the force)
A force causes CHANGE in the MOTION of an object.
all forces have agents* and objects**
*A specific and identifiable cause.
These can be animate or inanimate –
if you can’t name an agent – it’s not a force!
Ex: gravity – earth’s mass Ex: friction – microscopic roughness of
surfaces
**the victim of the force.
two main types of forces
• contact
• long-range
(at-a-distance/field)
tension applied spring
friction air resistance
normal (support) – perpendicular to
a surface
Nuclear (strong)
magnetic
electrical
Gravitational
(weight)
strongest
Range (meters)
Strong 2x10-15
Electromagnetic infinity
Weak 10-18
Graviational infinity
hank green strong force
strong force part 2
gravitational force
ex: designed for cornering
suspension design
421 meters (1,380 ft)
Jin Mao tower,
China, 1998 #10
#9 Trump Tower,
Chicago 2009
423 meters (1,388 ft)
Guangzhou International Finance Center,
China, 2010 #8
440.2 meters tall (1,444 ft)
#6
Nanjing Greenland Financial Center,
China, 2010
450 meters (1,480 ft)
#5
Petronas Towers, Malaysia,
1998
451 meters or 1,482 ft
#7 Willis Tower,
Chicago, 1974
527 meters (1,730 ft)
International Commerce Center,
Hong Kong, 2010
484 meters (1587 ft)
#4
#3
Shanghai World Financial Center,
China, 2008
494.4 m (1,622.0 ft)
#2
509.2 m (1,670.6 ft)
Taipei 101, Taiwan, 2004
World Trade Center, New York,
1970 (N. tower) 1972 (S. tower)
In order to create the 16-acre World Trade Center site, five streets were closed off and
164 buildings were demolished. Construction required the excavation of more than 1.2
million cubic yards of earth, which was used to create 23.5 acres of land along the
Hudson River, now part of Battery Park City in lower Manhattan. During peak
construction periods, 3,500 people worked at the site. A total of 10,000 people worked
on the towers; 60 died during its construction.
• Became the world’s tallest buildings • Had its own zip code • Each tower – 110 floors • 1,368 ft.
In 1993 terrorists drove a truck packed with 1,100 lbs of explosives into the
basement parking garage at the World Trade Center. The blast left a crater 22 ft
wide and 5 stories deep—only 6 people were killed and 1,000 injured. The towers
were repaired, cleaned, and reopened in less than a month.
Not the first attack…
In Feb. 2003, architect Daniel
Libeskind's design was
chosen for rebuilding the 16-
acre site of the former World
Trade Center. 1 World Trade,
which will be a symbolic
1,776 feet tall from the
ground to the top of its spire
is scheduled to open in 2013
(making it the 2nd tallest
building in the world).
#1 tallest building in the world (completed 2010)
The tallest man made structure sits in the heart of UAE, Dubai. Its former name was Burj
Dubai but was changed when the president of Abu Dhabi (Khalifa Bin Zayed) loaned
Dubai $10 billion since Dubai was drastically effected by the recent recession. The name
was changed in his honor. Getting and office would set you back a staggering $ 43,000
per sq m.
• Height: 828 m (2,717 ft)
• Floors: 163
• Completion: 2010
• Floor area: 517,240 m sq
• Estimated cost: USD $ 1.5 billion
• Designed by: Adrian Smith
Burj Khalifa, Dubai United Arab Emirates
http://www.engineeringinteract.org/resourc
es/parkworldplot/flash/concepts/allaboutfor
ces.htm
Newton explained how forces influence motion.
youtube
Newton’s 1st Law of Motion
Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
Galileo’s “Law of Inertia”.
How are force, mass and acceleration related?
Want to know the
secret to the
Force….
youngling,
younglings gather
round…
use equations
you must
How does acceleration depend on force?
How does acceleration depend on the object?
Can you write a rule from your PHET experimentation?
The relationship between an object’s mass m,
its acceleration a,
and the applied force F, is
m F = a
Newton’s 2nd Law of Motion
The relationship between an object's mass m, its
acceleration a, and the applied force F is F = ma.
Acceleration and force are vectors; in this law the direction of the force vector is the same as the direction of the acceleration vector.
The original version: When a force acts on an object, the object accelerates in the direction of the force. If the mass of an object is held constant, increasing force will increase acceleration. If the force on an object remains constant, increasing mass will decrease acceleration. In other words, force and acceleration are directly proportional, while mass and acceleration are inversely proportional.
F = ma – a quick history
Technically, Newton equated force to the differential change
in momentum per unit time. Momentum is a characteristic of
a moving body determined by the product of the body's
mass and velocity.
To determine the differential change in momentum per unit
time, Newton developed a new type of math -- differential
calculus. His original equation looked something like this:
F = (m)(Δv/Δt)
Because acceleration is defined as the instantaneous
change in velocity in an instant of time (Δv/Δt), the equation
is often rewritten as:
F = ma How Stuff Works
This equation form of Newton's second law allows us to specify a
unit of measurement for force. Because the standard unit of mass is
the kilogram (kg) and the standard unit of acceleration is meters per
second squared (m/s2), the unit for force must be a product of the
two -- (kg)(m/s2). This is a little awkward, so scientists decided to use
a Newton as the official unit of force. One Newton, or N, is
equivalent to 1 kilogram-meter per second squared. There are 4.448
N in 1 pound.
How Stuff Works
F = ma lets you quantify
motion of every variety
Let's say, for example,
you want to calculate
the acceleration of the
dog sled shown here.
modify the force equation to get a = F/m. When you plug in the numbers for force (100
N) and mass (50 kg), you find that the acceleration is 2 m/s2.
Units
Fnet = m a
1 N = 1 kg m/s2
The SI unit of force is the Newton*.
A Newton is about a quarter pound.
1 lb = 4.45 N
*Amount of force acting on a 1 kg mass to produce acceleration of 1 m/s/s)
Now let's say that the mass of the sled stays at 50 kg and that
another dog is added to the team. If we assume the second dog
pulls with the same force as the first (100 N), the total force would be
200 N and the acceleration would be 4 m/s2
Notice that doubling the force by adding another dog doubles the acceleration. Oppositely,
doubling the mass to 100 kg would halve the acceleration to 2 m/s2.
Finally, let’s imagine that a second dog team is attached to the sled
so that it can pull in the opposite direction.
If two dogs are on each side, then the total force pulling to the left (200 N) balances
the total force pulling to the right (200 N). That means the net force on the sled is zero,
so the sled doesn’t move.
Newton's second law is concerned with net forces.
We could rewrite the law to say: When a net force acts on an object, the
object accelerates in the direction of the net force.
Now imagine that one of the dogs on the left breaks free and runs away.
Suddenly, the force pulling to the right is larger than the force pulling to the
left, so the sled accelerates to the right.
What's not so obvious is that the sled is also
applying a force on the dogs. In other words, all
forces act in pairs. This is Newton's third law…. How Stuff Works
What is Net Force?
When more than one
force acts on a body,
the net force
(resultant force) is the
vector combination of
all the forces, i.e., the
“net effect.”
F1
F2
F3
Fnet
Net Force & the 2nd Law For a while, we’ll only deal with forces that are
horizontal or vertical.
When forces act in the same line, we can just
add or subtract their magnitudes to find the
net force.
2 kg
15 N 32 N
Fnet = 27 N to the right
10 N
a = 13.5 m/s2
? What is the acceleration of the object ?
A karate chop can break a 3.8 cm thick concrete block by moving the hand at 11 m/s, creating 3069 N force.
The bones of the hand can
withstand 40X that force.
check your understanding…
Let’s assume that the wheels of a 5-kg car apply 10 N of
force. What is the net force if friction and drag are
negligible?
Mass = 5 kg
The net force would equal 10 Newtons.
What is the acceleration of the car?
F = ma 10 = 5a
acceleration = 2m/s2
What is the net force if the wheels of the
5-kg car apply 10 Newtons but a 1-kg
parachute applies 3 Newtons in the
other direction?
The net force would equal 3 N
(the total mass = 6 kg)
What is the acceleration of the car?
a = F/m a = 3/6
acceleration = 0.5 m/s2
A rocket is added to the car and
applies an additional force of 10
Newtons. The wheels still apply 10
N. What is the net force if the
parachute continues to apply 7
Newtons in the other direction?
The total mass of the car, rocket
and parachute is 10 kg.
The net force would equal 13 Newtons. The total mass = 10 kg.
What is the acceleration of the car?
a = F/m a = 13/10
acceleration = 1.3 m/s2
Newton’s 3rd Law of Motion
For every action, there is an equal and opposite reaction.
OR “The mutual actions of two bodies upon
each other are always equal, and directed to
contrary parts”.
An example from nature…
The size of the force on the water equals the size of the force on the fish; the
direction of the force on the water (backwards) is opposite the direction of the
force on the fish (forwards). For every action, there is an equal (in size) and
opposite (in direction) reaction force.
Consider the propulsion of a fish through the water.
A fish uses its fins to push
water backwards. But a
push on the water only
accelerates the water.
Since forces result from
mutual interactions, the
water must also be pushing
the fish forwards, propelling
the fish through the water.
I love
Newton’s 3rd
Law
Check your understanding:
While driving down the road, a firefly
strikes the windshield of a bus in front
of the face of the driver. This is a clear
case of Newton's third law of motion.
The firefly hit the bus and the bus hits
the firefly. Which of the two forces is
greater: the force on the firefly or the
force on the bus?
A force represents the interaction of an object
(system) with its environment (where the force is
being exerted on the system) by an agent (the cause
of the force)
A net force causes CHANGE in the MOTION of an object.
Galileo (1630’s) concluded “it is not the nature of an
object to stop once it is set in motion; rather, it is an
object’s nature to maintain its state of motion.”
Newton (1687) further developed this
concept to become his First Law of Motion.
“An object in motion tends to stay in motion;
an object at rest tends to stay at rest unless it
experiences a net external force.”
1st Law
• A moving body will continue moving in the same direction with the constant speed until some net force acts on it.
• A body at rest will remain at rest unless a net force acts on it.
• Summing it up: It takes a net force to change a body’s velocity.
Inertia Example 1
An astronaut in
outer space will
continue drifting
in the same
direction at the
same speed
indefinitely, until
acted upon by an
outside force.
Inertia Example 2 If you’re driving at 65 mph and have an
accident, your car may come to a stop in
an instant, while your body is still moving
at 65 mph. Without a seatbelt, your inertia
could carry you through the windshield.
1st Law: Law of Inertia
The tendency of an object not to
accelerate.
“In the absences of forces, a body will preserve its state of
motion.”
The egg drop
challenge
“When the net external force on an object is zero, its acceleration (or the change in its motion) is zero.”
Myth Busters
Determining Net Force
When more than one
force acts on a body,
the net force
(resultant force) is the
vector combination of
all the forces, i.e., the
“net effect.”
F1
F2
F3
Fnet
consider…
Fresistance
vector Fforward represents forward force of car, Fresistance acts in opposite direction,
backward force air exerts on car to resist motion. The vector Fgravity represents
downward force of gravity and vector Fnormal, represents the upward force the ground
exerts on the car.
Fforward
Fgravity
All 4 forces are external forces acting on the car. The net external
force* is the vector sum of all the forces acting on a body. Defined as
“the total force resulting from a combination of external forces on an
object”.
*sometimes called the resultant force, found using methods for finding resultant vectors.
consider…
If both teams pull on the rope with equal but opposite force, the
net external force is zero. A knot in the center would remain at
rest even though forces are pulling in opposite directions.
If one side increases the force, the knot experiences a net
external force equal to the difference in the forces – it moves in
the direction of the greater pull.
1st law – inertia is an object’s resistance to change in
velocity
The force that brings an accelerating object to equilibrium must be = and opposite to the force causing the acceleration.
An object is in
equilibrium if it
is at rest OR
moving at
constant velocity
Fnet = 0
From 1st law: an object with no net external
forces is in a state of equilibrium.
How much does a
known force affect the
motion of an object?
more free body diagram practice
practice problems 7-11, pg. 124
worksheet
review what we know so far
common misconceptions
pg. 125
• When a ball has been thrown, the force of the
hand that threw it remains on it.
• A force is needed to keep an object moving.
• Inertia is a force.
• Air does not exert a force.
• The quantity ma is a force.
Graph of F vs. a
In the lab various known forces are applied—
one at a time, to the same mass—and the
corresponding accelerations are measured.
The data are plotted. Since F and a are
directly proportional, the relationship is linear.
F
a
What does the slope of the line represent?
Slope
F
a
Since slope = rise / run = F / a, the slope is
equal to the mass.
(Or, think of y = m x + b, (like in algebra). y corresponds
to force, m to mass, x to acceleration, and b (the y-
intercept) is zero.)
F
a
2nd Law: Fnet = m a • The acceleration an object undergoes is directly
proportion to the net force acting on it.
• Mass is the constant of proportionality.
• For a given mass, if Fnet doubles, triples, etc. in size, so does a.
• For a given Fnet if m doubles, a is cut in half.
• Fnet and a are vectors; m is a scalar.
• Fnet and a always point in the same direction.
• The 1st law is really a special case of the 2nd law (if net force is zero, so is acceleration).
Net Force & the 2nd Law dealing with forces that are horizontal or vertical is straight
forward:
When forces act in the same line, we can just add
or subtract their magnitudes to find the net force.
2 kg
15 N 32 N
Fnet = 27 N to the right
10 N
a = 13.5 m/s2
? What is the acceleration of the object ?
1st law – inertia (if net force is 0 so is acceleration)
2nd law – the acceleration of an object is proportional to the
net force acting on it
The force that brings an accelerating object to equilibrium must be = and opposite to the force causing the acceleration.
(applying Newton’s 3rd law)
An object is in
equilibrium if it is at
rest OR moving at
constant velocity
Fnet = 0
You know: Force is exerted on an object when that object interacts with some other object.
Forces always act in pairs.
“Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force
on the first object.
In other words: if there is a Force F on the surface of
an object such as the golden ball above, then there is
an equal and opposite force exerted back at the same
point. This equal and opposite force is often given by
negative F (-F).
when the boxer kicks the golden ball
with a force F, there is an equal and
opposite force (-F) being applied back
at his foot.
• If you hit a tennis ball with a racquet, the force on the ball due to the racquet is the same as the force on the racquet due to the ball, except in the opposite direction.
• If you catch a ball, the force of the ball on the glove is the same as the force of the glove on the ball.
Examples:
Action - Reaction • If you drop an apple, the Earth pulls on the
apple just as hard as the apple pulls on the Earth.
• If you fire a gun, the bullet pushes the gun backwards just as hard as the gun pushes the bullet forwards.
“For every action there’s an
equal but opposite reaction.”
Earth / Apple How could the forces on the tennis ball, apple, and bullet, be
the same as on the racquet, Earth, and rifle? The 3rd Law
says they must be, the effects are different because of
the 2nd Law!
Earth
apple
3.92 N
3.92 N
0.40 kg
5.98 1024 kg
A 0.40 kg apple weighs 3.92 N
(W = mg). The apple’s weight is
Earth’s force on it. The apple
pulls back just as hard. So, the
same force acts on both bodies.
Since their masses are different,
so are their accelerations (2nd
Law). The Earth’s mass is so
big, it’s acceleration is negligible.
Earth / Apple (cont.)
a = m m a
Apple’s big
acceleration
Apple’s
little mass Earth’s little
acceleration
Earth’s
big mass
The products are the same, since the forces are the same.
Demolition Derby
When two cars of
different sizes collide,
the forces on each are
the SAME (but in
opposite directions).
However, the same
force on a smaller car
means a bigger
acceleration!
Swimming Due to the 3rd Law, when you swim you push the water
(red), and it pushes you back just as hard (blue) in the
forward direction. The water around your body also
produces a drag force (green) on you, pushing you in the
backward direction. If the green and blue cancel out, you
don’t accelerate (2nd Law) and maintain a constant velocity.
Note: The red vector is a force on the water, not the on
swimmer! Only the green and blue vectors act on the swimmer.
action-reaction pairs
The two forces
act at the same
time. Don’t necessarily
result in
equilibrium (can be
unbalanced).
Force of the
wood on the nail
Force of hammer
on the nail
ACTION: She’s pushing the
wall
REACTION: The wall
pushes back.
Will she accelerate?
YES! The force from wall
will push her to the left.
What is the ACTION-REACTION pair here?
Newton’s 3rd Law
How you touch the world is how the world touches you.
(you cannot touch without being touched)
question this…
Could a sky diver fall with enough force to launch a
child off a see-saw 7 stories into the air?
Identify the action-reaction pairs in the following:
a. A person takes a step
b. A snowball hits someone in the back
c. A person rowing a boat
Person pushes on ground, ground pushes on the person.
Snowball on the back, back on the snowball.
Oar in the water, water on the oar.
Quick review: forces song
A 6.0 kg object undergoes an acceleration of
2.0 m/s2.
a. What is the magnitude of the net external
force acting on it?
b. If this same force is applied to a 4.0 kg
object, what acceleration is produced?
12 N F=ma F = (6.0)(2)
3 m/s2 F=ma 12 = (4)(x)
A phonebook is resting on the table. We know gravity is pulling on it with 30 N, what must be the magnitude of the table’s force (FN) holding up the phonebook?
FNet = FN - Fg
= (30 N)(9.8 m/s2) = 293 N
A child pulls a wagon with a horizontal force, causing it
to accelerate. Draw a free body diagram showing the
acceleration of the wagon.
F pulling
F friction
The forces on a sailboat are 390 N north and 180 N east.
If the boat and crew has a mass of 270 kg, what are the
magnitude and direction of their acceleration?
270 kg
180 N
390 N
Fnet
θ
Θ = tan-1 390 = 65°
180
Fnet = √(390)2 + (180)2
= 429.5
a = 429.5 = 1.6 m/s2
270
1.6 m/s2 at 65° N of E
WEIGHT THE MAGNITUDE OF THE FORCE OF GRAVITY ON AN OBJECT
Remember that “scientifically
speaking”, mass isn’t related to size.
Mass is related to how much an object
resists changes to its state of motion.
Weight is caused by gravitational acceleration.
Gravitational force
The equation for gravitational force is:
FG = Mass x Gravity = mg. Or W = mg
The value of “g” (the strength of the gravitational field) is unique to each planet.
While g here on Earth may be ~10 m/s2, on Jupiter, g ~25 m/s2 and on the Moon,
g is only ~ 1.6 m/s2.
All masses near Earth feel a
gravitational force proportional
to their mass: the bigger the
mass, the bigger the
gravitational force.
W = mg
• Weight = mass acceleration due to gravity.
• This follows directly from F = m a.
Near the surface of the
Earth,
g = 9.8 m/s2.
Fg = mg
Gravitational force is associated with acceleration
in the direction of that force.
Simply put, an object subject to a gravitation force will
“fall” in the same direction in which the force is acting.
Weight will change based on whether there
are forces acting that increase or
reduce the “upward” force
necessary to balance out the
“downward” gravitational force;
for instance the buoyant force that
helps an object float in water,
making it “weightless”.
The force it takes to counteract and balance out Fg is the object’s
“weight.”
Weight = mass acceleration due to gravity
If an object is pushed upwards so that it accelerates up, it’s
weight on the surface pushing it up will increase.
Alternatively, if the object is allowed to fall, it’s weight will be
reduced.
when you’re in an elevator your weight changes because you are experiencing
an upward or downward acceleration, so your weight does not completely offset
the gravitational force.
Another example: an object’s weight changes due to it’s acceleration
relative to the gravitational field.
your weight is the net force
required to counteract the
downward force such that you
experience a certain
acceleration, and that value
can change even though the
gravitational force remains the
same
do the math…
Example problem pg. 128
Your mass is 75 kg. You stand on a bathroom scale in an
elevator going UP. Starting from rest, the elevator
accelerates at 2.0 m/s2 for 2.0 s, then continues at a
constant speed. What is the scale reading (your weight)
during the acceleration?
Draw the free body diagram.
Which direction is the net force?
Calculate…..
What do you know? m = 75 kg a = +2.0 m/s2
Fnet is sum of the Fscale on you and the Fgravity acting in the opposite direction Fnet = Fscale - Fgravity
Fscale = Fup + Fgravity Fscale = ma + mg Fscale = m(a + g) = 75(2.0 + 9.8) = 890 N
In a lecture delivered in Kyoto in 1922,
Einstein described that moment of
epiphany he had in 1907: "I was
sitting in the patent office in
Bern when all of a sudden a
thought occurred to me: If a
person falls freely, he won't
feel his own weight. I was
startled. This simple thought
made a deep impression on
me. It impelled me toward a
theory of gravitation."
When astronauts are in the space station, their mass is the same
as it is on Earth.
The gravitational force on the space station is only slightly less
than the gravitational force on Earth.
The space station, and everything in it, is subject to Earth’s gravity
(that’s what keeps it in orbit).
Because the station (and
everything on it) moves together
around Earth, the space station
and its contents are constantly
Falling towards Earth; they are
In free fall.
Weightlessness
The station and its contents are
weightless since no force is
exerted to counterbalance the
gravitational force.
Based on what it means for
something to have weight, this
explains why – despite having
mass and despite being subject
to a gravitational force – the
astronauts are weightless.
They never fall to Earth, since the curvature of Earth
exactly matches the shape of the orbit, but they are
constantly falling, nonetheless.
NASA - mass vs weight intro
Demonstrating acceleration based on mass in microgravity.
Accelerating Mass - NASA
Tools such as hammers, and levers are designed to make work easier.
Sometimes, the environment in which a person works dictates whether or
not a certain tool will get the job done. In the microgravity environment of
space, astronauts are often required to do experiments or simple repairs.
On Earth, gravity helps anchor a person to the ground, making tightening a
bolt a rather simple activity. Engineers have had to develop different types
of bracing systems — a whole new set of tools — to assist astronauts
working in space.
Using Gravity
Using tools in space
Forces and the motion they create are fundamental concepts in the fields of civil,
materials and mechanical engineering. Engineers must account for forces when
designing roadways and buildings, since these structures must not fail under their
own weight of construction materials, the weight of people and equipment on them,
and environmental loads (vibrations, wind drag, etc.).
Galloping Gertie, Tacoma, Nov. 7, 1940
galloping gertie
lateral forces
Lateral forces are those directed at the side of the
structure. These forces include those generated by
things such as the wind, earthquakes, and
explosions.
As a system, a structure must be designed so that it can resist all forces
to which it is subjected.
Great Science Project Ideas, J. VanCleave
tension gravity forces (weight)
compression
a force that pushes materials together
a force that pulls materials apart
the weight of the bridge as well as the weight of the car causes the beam to
bend. The top edge of the beam has shortened because the compression
forces, squeezing the materials together. The bottom edge of the beam has
lengthened due to tension forces, stretching the material.
Stress and Strain
The term stress (s) is used to express the loading in terms of force applied
to a certain cross-sectional area of an object.
From the perspective of loading, stress is the applied force or system of
forces that tends to deform a body.
From the perspective of what is happening within a material, stress is the
internal distribution of forces within a body that balance and react to the
loads applied to it.
The stress distribution may or may not be uniform, depending on the nature
of the loading condition.
Stress is often represented as a vector quantity for many engineering
calculations and for material property determination. For example, the
stress in an axially loaded bar is simply equal to the applied force divided
by the bar's cross-sectional area.
Some common measurements of stress are:
Psi = lbs/in2 (pounds per square inch)
ksi or kpsi = kilopounds/in2 (one thousand or 103 pounds per square
inch)
Pa = N/m 2 (Pascals or Newtons per square meter)
kPa = Kilopascals (one thousand or 103 Newtons per square meter)
is the response of a system (object) to an applied stress.
When a material is loaded with a force, it produces a stress, which then
causes a material to deform.
Engineering strain is defined as the amount of deformation in the direction
of the applied force divided by the initial length of the material.
For example, the strain in a bar that is being stretched in tension is the
amount of elongation or change in length divided by its original length.
Strain
If the stress is small, the material may only strain a small amount and
the material will return to its original size after the stress is released.
This is called elastic deformation, because like elastic it returns to its
unstressed state.
If a material is loaded beyond it elastic limit, the material will remain in
a deformed condition after the load is removed. This is called plastic
deformation.
Why giant moles can’t exist
the mole people
Biophysics
F
e
m
u
r
The strength of a bone, like a femur, is proportional to
its cross-sectional area, A. But an animal’s weight is
proportional to its volume.
Giant ants and moles from sci-fi movies couldn’t exist
because they’d crush themselves!
Here’s why: Suppose all dimensions
are increased by a factor of 10. Then
the volume (and hence the weight)
becomes 1000 times bigger, but the
area (and hence the strength) only
becomes 100 times bigger.
A real life example:
Basketball players, because of their
height, tend to suffer many stress
fractures;
and elephants have
evolved proportionally
bigger femurs than deer.
The Atwood machine invented in 1784 by Rev. George Atwood as a laboratory experiment to verify the mechanical laws of motion with constant acceleration.
The ideal Atwood Machine consists of two
objects of mass m1 and m2, connected by
an inextensible massless string over an
ideal massless pulley.
When m1 = m2, the machine is in neutral
equilibrium regardless of the position of the
weights.
When m1 ≠ m2 both masses experience
uniform acceleration.
Solving Atwood Machine Problems
requires that you calculate the
acceleration of the system of
weights.
Using Newton’s 2nd law: F = mass X acceleration.
The difficulty of Atwood machine
problems lies in determining the
tension force on the string.
m1
FT
Fg
heavier
weight
lighter
weight
Both weights have
tension forces pulling up.
Both weights have gravity
forces pulling down.
The force of gravity is equal to the mass ("m1" for weight 1 and "m2" for weight 2)
of the weight times "g" (equal to 9.8). Therefore, the gravitational force on the
lighter weight is m1*g, and on the heavier weight is m2*g.
m1
m2
Calculate the net force acting on the lighter weight:
Fnet = FT – (m1*g)
(since they pull in opposite directions)
m1
FT
Fg
Calculate the net force acting on the heavier weight:
Fnet = (m2*g) - FT
On this side, tension is subtracted because the direction of tension
is opposite on opposite sides of the pulley. This makes sense if
you consider the weights and string laid out horizontally -- the
tension pulls in opposite directions.
m2
FT
Fg
Substitute (FT - m1*g) in for the net force in the equation
Fnet = ma (Newton's 2nd law)
FT - m1*g = m1*a or Tension = m1*g + m1*a.
Substitute this equation into the equation for m2 : Fnet = (m2*g) - FT
Fnet = (m2*g) - (m1*g + m1*a)
By Newton's 2nd law, Fnet = m2*a
By substitution, m2*a = (m2*g) - (m1*g + m1*a)
Find the acceleration of the system by solving for a:
a*(m1 + m2) = (m2 – m1)*g
so, a = (m2 – m1)*g/(m1 + m2)
In other words, the acceleration is equal to 9.8 times
the difference of the two masses, divided by the sum
of the two masses.
a = 9.8(m2 – m1)
(m2 + m1)
If you think about it, gravity is
accelerating only the difference in
the masses because otherwise, the
system is in static equilibrium.
Static friction The friction that exists between two surfaces that are
not moving relative to each other.
Kinetic friction The friction that exists between two surfaces that are
moving relative to each other.
There are two kinds of friction, based on how the two surfaces are moving relative to each other:
In any situation, the static friction is greater than
the kinetic friction.
Frictional Forces Occur When Materials are
in Contact
W
fs F
N
Surfaces in
Contact
M1
Spring Scale
F = Force Causing Motion (Pull on Scale)
Fs = Force of Static Friction (Resists Motion)
N = Force Normal Holds Surfaces in Contact
W = Weight of Object ( Mass x Gravity)
Friction is a Force That Resists Motion
W
fs F
N
Surfaces in
Contact
The pink block M1 will not move until the
force, F (pull on the scale ) exceeds the force of
Static Friction fs.
M1
Spring Scale
The relative force of static friction between 2 objects is
expressed as the quotient of the force required to
move the object (F) divided by the weight (W) of the object.
W
fs F
N
Surfaces in
Contact
M1
Spring Scale
This is the Coefficient of Friction
s
FW
= Force Required to Cause Motion
= Weight of Object
= Coefficient of Friction
W
Fs Coefficient of Static Friction
W
fs F
N
Surfaces in
Contact
M1
Spring Scale
The coefficient of static friction between the
surface and the battery is described
algebraically:
W
Fs
= 580
= 110
s = .190
W
Fk
The coefficient of Kinetic Friction can be found
using the same technique.
Record the force required to move the battery at
a constant rate.
Friction is also proportional to the normal force, which is how we'll
be able to calculate it.
The actual formula for friction is…
Ff = μ FN
Ff = force due to friction (Newtons)
FN = normal force (Newtons)
μ = (Greek letter “mu”) coefficient of friction between two
surfaces (no units)
μs is static, μk is kinetic
Obviously, some surfaces have less
friction than others…
When we measure the coefficient of friction (μ), the smaller the number, the less the friction between the two surfaces.
You will be able to use a table of
predetermined values, or calculate it.
Ff,kinetic = μk FN
0 < Ff,static < μsFN
2 formulas:
The static friction force can vary from 0 to μsFN -
max static frictional force which must be overcome
before motion can begin.
Static friction between the
block and the floor
example:
A 12kg piece of wood is placed on top of another piece of
wood. There is 35N of static friction measured between
them. Determine the coefficient of static friction between
the two pieces of wood.
First calculate FN FN = Fg = mg
= (12kg) (9.81m/s2)
μs = Ff / FN
= (35N) / (117.7 N)
μs = 0.30
12 kg
FN = 117.7 N
Then use this answer to calculate Ff ... Ff = μs FN
A steel box (mass of 10 kg) is sitting on a steel workbench. Can the box be pushed out of the way with a force of 25 N?
try another example
Calculate the max. force due to static friction…
a) Draw a free body diagram of the box.
figure out the normal force… FN = Fg = mg = (10 kg) (9.81 m/s2) FN = 98 N
…use that to calculate the maximum static friction.
(the values for μs and μk are given)
for steel on steel, μs is 0.74 and μk is 0.57
Ff = μs FN
= 0.74 (98 N)
Ff = 73 N
So, does this mean that when the box is pushed with
Fa = 25 N, the friction will push back with 73 N?
No!
The force due to static friction can go up to a
maximum of 73 N, but can also be less.
It will be equal to whatever the Fa is, up to the maximum
calculated here.
Ff = Fa = 25 N (they just point in opposite directions) FNET = Zero With no net force acting on it, the box will not start to move.
What if the push is a force of 73 N? will
anything will happen?
This exactly equals the maximum static frictional force between these two surfaces.
Ff = Fa = 73 N (but in opposite directions!) FNET = Zero With no net force acting on it, the box will not start to move.
In order to move -- you must overcome
static friction.
If a push is a force of 100 N , determine if anything
will happen.
This applied force is greater than the static friction,
so it will start to move… but remember that we will
now be using kinetic friction!
Ff = μk FN = 0.57 (98 N) Ff = 56 N
FNET = FN + Ff = 100 + -56 FNET = 44 N
FNET = ma a = FNET / m = 44 / 10 a = 4.4 m/s2
The box will accelerate at 4.4 m/s2.
Try some problems:
A rightward force is applied to a 6-kg object to move it
across a rough surface at constant velocity. The object
encounters 15 N of frictional force. Use the diagram to
determine the gravitational force, normal force, net force,
and applied force. (Neglect air resistance.)
Since there is no vertical acceleration, the normal force
equals the gravity force.
Since there is no horizontal acceleration, Ffrict = Fapp = 15 N
Fnet = 0 N; Fgrav = 58.8 N; Fnorm = 58.8 N; Fapp = 15 N
When the velocity is constant,
a = 0 m/s2 and Fnet = 0 N
Since the mass is known,
Fgrav can be found:
Fgrav = m • g = 6 kg • 9.8 m/s/s =
58.8 N
A rightward force is applied to a 5-kg object to move it
across a rough surface with a rightward acceleration of 2
m/s2. The coefficient of friction between the object and the
surface is 0.1. Use the diagram to determine the
gravitational force, normal force, applied force, frictional
force, and net force. (Neglect air resistance.)
Fnet =10 N, right; Fgrav = 49 N; Fnorm = 49 N; Ffrict = 4.9 N; Fapp = 14.9 N
Fnet can be found using Fnet = m • a
= (5 kg) • (2 m/s/s) = 10 N, right.
Since the mass is known, Fgrav can be
found: Fgrav = m • g = 5 kg • 9.8 m/s2 =
49 N
Since there is no vertical acceleration, the normal force equals the gravity
force.
Once Fnorm is known, Ffrict can be found using Ffrict = μ • Fnorm
= (0.1) • (49 N) = 4.9 N.
Since the Fnet = 10 N, right, the rightward force (Fapp) must be 10 N more
than the leftward force (Ffrict); thus, Fapp must be 14.9 N.
In a Physics lab, Bob and Joe apply a 34.5 N rightward
force to a 4.52-kg cart to accelerate it across a
horizontal surface at a rate of 1.28 m/s2. Determine the
friction force acting upon the cart.
Ffrict = 28.7 N, left
The net force can be determined from the mass and acceleration of the sled.
Fnet = m • a = (4.52 kg) • (1.28 m/s2) = 5.7856 N, right.
Since the net force is in the direction of the applied force, then the applied
force must be greater than the friction force. The friction force can be
determined because the net force is the vector sum of all the forces. So
5.7856 N, right = 34.5 N, right + Ffrict. Therefore,
Fn
Fg
Fapp Ff
Since there is no vertical acceleration,
normal force = gravity force.
Fgrav = m • g = (4.525 kg) • (9.8 m/s2) = 44.296 N
Example Problems, pg. 131-132
Practice problems 14-16, pg. 133
Read/study pgs. 134 - 143
Finish calculations.
Answer questions – turn in!
Periodic motion
Back and forth over the same path.
Vibrating
Tuning fork
200
grams
200
grams
A weight on
a spring
A boy on
a swing
Simple Harmonic Motion
Simple harmonic motion (SHM) refers to a Periodic Motion which repeats itself at regular, equal intervals of time.
SHM describes the behavior of many physical
phenomena: – a pendulum – a bob attached to a spring – low amplitude waves in air (sound), water, the ground – the electromagnetic field of laser light – vibration of a plucked guitar string – the electric current of most AC power supplies
Simple Harmonic Motion
• The force causing the motion is in direct relationship to the displacement of the body.
• The displacement, velocity, acceleration and force are specific at various points in the cycle.
SHM
• Equilibrium: the position at which no net force acts on the object.
• Displacement: The distance of the object from its equilibrium position.
• Amplitude: the maximum distance the object moves from equilibrium.
Springs and SHM
Attach an object of mass m to the end of a spring, pull it out to a distance A, and let it go from rest. The object will then undergo simple harmonic motion. The spring demonstrates
SHM because it vibrates
back and forth around its
unstretched position.
F elastic The direction of the
force acting on the
mass (F elastic) is
opposite the direction
of displacement from
equilibrium.
F elastic
F elastic
Direction of the spring force is always opposite the direction of the mass’ displacement.
Restoring Force
The spring force always pushes/pulls the mass
back to its original equilibrium position
(restoring force).
Robert Hooke (1678)
First defined this relationship
between mass/displacement of
a spring system.
Hooke’s Law
Felastic = -kx
Spring force = -(spring constant)(displacement)
The Simple Pendulum
• The pendulum bob is clearly oscillating as it moves back and forth – but is it exhibiting SHM?
Amplitude:
max.
displacement
from
equilibrium (m,
radian)
Period, T :
time it takes to
execute a
complete cycle
of motion (s)
Frequency, f :
number of
cycles or
vibrations per
unit of time
(Hz)
Calculations of the period and frequency are different
than the mass-spring system because they depend on
different physical factors.
(for small angles)
neither mass
nor amplitude
affect the period
θ
But changing the string length does
Also – a change in the free fall acceleration!
Galileo is credited as the first
person to notice that the motion
of a pendulum depends on its
length and is independent of its
amplitude (for small angles)
Measured the frequency by timing
the swings with his pulse.
Why does period depend on string length?
When 2 pendulums have
different length but same
amplitude, shorter
pendulum has a smaller
arc to travel.
The distance to
equilibrium is less while
the acceleration remains
the same --- so the
shorter length will have a
shorter period.
Why don’t mass and amplitude affect the period?
When the bobs differ in
mass, the heavier
provides a larger
restoring force, but also
needs larger force to
achieve the same
acceleration.
Because the
acceleration of
both is the same,
the period for both
is the same.
ex. problem:
What is the period of a 3.98
m long pendulum?
What is the period of a
99.4 cm long
pendulum?
4.0 s
2.0 s
A washer on a string swings
back and forth once every
1.0 s. How long is the
string? 0.25 m
T = 1.0 s
g = 9.81 m/s/s
T√g = √L
2π T2g = L
4π2