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Physics – Motion and Energy
Here’s what you will know when you are done with this unit!
I. Review motion in one dimension by analyzing how distance, displacement, speed, velocity acceleration and time interrelate with each other. II. Determine the difference between a vector and scalar quantityIII. Use scientific principles to solve a problem by using a technological design. IV. Understand and use changes in variables that affect a system to solve problems.V. Understand the forms of energy found in our natural world. VI. Understand how energy can change forms but never be lost
VII. Explore how kinetic and potential energy can be used to solve problems
Everybody uses physics everyday on a simple level. When ever we try to solve a problem in the physical world we use physics to solve the problem.
This could be from throwing down sand and salt on ice to knowing which way to push to run forward.
Most of the things in Physics we have intuitively learned when we were just a few years old. This year we will try to explain why they work.
Who Uses Physics?
In physics, if we are to ask questions we should try to consider everything
To describe motion accurately and completely, a coordinate system is necessary.
Coordinate system tells you the location of a zero point of the variables you are studying and the direction in which the values of the variables increase.
An example of this is a graph or a map
Coordinate systems
A. Motion Diagram (1D) Indicate the position of something at equal
intervals of time Ex.
1s 2s 3s 4s 5s
How Things Move
Vectors – quantities that have both size (also called magnitude) and a direction
Ex – velocity (meters per second north)
Scalars – quantities that have only magnitude
Ex – speed- (meters per second)
Vectors and Scalars
Movement in relation to a frame of reference.
Example – people in a car look like they are moving to somebody standing on the road, but that person doesn’t seem to be moving when looking at somebody right next to them
Relative Motion and Frame of reference
Distance – length of a path between two points
SI unit of distance is meters Scalar quantity – gives only magnitude Shows total amount of movement no matter
without concern for direction. Example - It’s five blocks away
Distance
Displacement – distance and direction Shows movement from where the object
started from Units are also meters Vector quantity – quantity that has magnitude
AND direction. Example – 5 blocks North
Displacement
When two displacements have the same directions they can be added.
When two displacements have different directions they can be subtracted.
When two or more displacements have different directions, they may be combined by graphing.
Resultant vector – the vector sum of two or more vectors.
Adding displacements
Speed is the distance traveled in a certain amount of time. It is a scalar quantity It does not tell you direction.
Scalar quantity s= Speed d= distance t = time
s = d/t
What is speed?
You Try!
If Johnny is riding 3 kilometers per hour on his skateboard, what is his speed in kilometers/hour?
3 kilometers/ hourIf Tanya can ride her bmx bike 10 miles in 2
hours, what is her speed in miles per hour? 5 miles / hour
If a space ship travels towards the sun 150,000 km per day, what is the speed in km/h?
6250 km/ h
Velocity is speed AND direction! v = velocity d = displacement ( this deals with direction also. t = time
v = d / t (don’t forget that you must include direction.
Velocity is a vector quantity
What is velocity?
v = ∆d / ∆ t = d1 – d0/ t1 – t0
= change
You try! Find the average velocity for a biker who biked 5 miles the first 10 minutes, 3 miles the second 10 minutes, and 1 mile the third 10 minutes. The biker was traveling east.
Average Velocity
Velocity within the time interval v = instantaneous velocity v = d / t within a certain localized time
interval.
Instantaneous velocity
How much something is speeding up or slowing down, changes in direction, or changes in both speed and direction.
Acceleration is a vector a = acceleration ∆v = change in velocity t = time interval a = v / t
Acceleration
Average acceleration is the average of the acceleration over an entire period of time
average acceleration equals the change in velocity divided by the change in time.
a = v/ t = vf – vi/ tf – ti
Average Acceleration
Find the acceleration of a foam ball dropping at 3 m/s in 1 second?
3 m/s2
Calculate the acceleration of a car (in km/h∙s) that can go from rest to 100km/h in 10 s.
(10 km/h·s)
You Try
Changing direction also is acceleration Since the object changes direction, the
vector of the object changes causing it to have a change in velocity in that plane which causes a change in acceleration.
Changing direction
Constant acceleration – there is a steady change in acceleration meaning that the velocity of an object changes by the same amount each second.
Acceleration
Free fall is the acceleration of an object towards the earth solely because of gravity
Objects that are near Earth’s surface accelerate at a rate of 9.8 m/s2 if we are in a vacuum.
Free Fall
Much more spectacular differences in the strength of gravity can be observed away from the Earth's surface:
Location g (m/s2) asteroid Vesta (surface)……….0.3 Earth's moon (surface)………..1.6 Mars (surface)………………...3.7 Earth (surface)………………..9.8 Jupiter (cloud-tops)……………26 Sun (visible surface)………….270 typical neutron star (surface)…1012 black hole (center)infinite according to some theories,
on the order of 1052 according to others
Comparing Gravity
There are three simple equations that can be used to help understand one relationship with another
Equation #1 Final Velocity = Initial velocity + acceleration x change in time or the formula
vf = vi + aΔt
Linking them all together
The square of the final velocity equals the sum of the square of the initial velocity and twice the product of the acceleration and the displacement since the initial time.
Vf2 = Vi
2 + 2a(df-di)
Equation #3
Nature of Energy
Energy is all around you! You can hear energy as sound. You can see energy as light. And you can feel it as wind.
What is work
Work is equal to the constant force exerted on an object in the direction of motion, times the object’s displacement
Measured in joules
W = Fd W = Δ KE
What is energy?
Energy is the ability of an object to produce a change in itself or the world around it.
Also defined as the change of work in a system
Kinetic Energy
The energy resulting from motion
Equal to ½ times the mass of the object multiplied by the speed of the object squared
KE = ½ mv2
Measured in joules Also useful is W = Δ
KE
Gravitational Potential Energy
Gravitational potential energy of an object is equal to the product of its mass, the acceleration due to gravity and the distance from the reference level.
PE = mgh Also measured in
joules
Elastic Potential Energy
The potential energy that may be stored in an object such as a rubber band, as a result of its change in shape
Examples: a pulled back rubber band, rubber balls, trampolines
Thermal Energy
A measure of the internal motion of an object’s particles
A change in an object’s thermal energy is measured with a thermometer
Kinetic-Potential Energy Conversions
As a basketball player throws the ball into the air, various energy conversions take place.
Potential Energy
Gravitational Potential Energy is energy due to an objects height above the ground
PE = mghm = massg = acceleration due to
gravityh = height
http://gaaf.com/pictures/200406_utah/image009.htm
Let’s Practice
A rock has a mass of 8.40 x 104 kg. The center of mass is 29.0 m above the ground. How much energy does it have?
PE = mghIdentify the variablesm= 8.40 x 104 kgg= 9.81 m/s2
h= 29.0 mPE = (8.4X104)(9.81)(29) = 2.39 x 107 J
http://gaaf.com/pictures/200406_utah/image009.htm
We call the sum of PE and KE mechanical energy.ME = KE + PE
Mechanical energy is important because it is conserved (as long as there are no non conservative forces, like friction)
Therefore, if one goes down, the other goes up by the same amount.
What’s so important about PE and KE?
Conservation of Energy
The law of conservation of energy states that in a closed, isolated system, energy can neither be created nor destroyed; rather energy is conserved
Energy just changes form from one to another while the total stays the same.
Conservation of Mechanical Energy
When mechanical energy is conserved, the sum of the kinetic energy and potential energy before an event is equal to the sum of the kinetic and potential energy after the event. KEb +PEb = KEa + PEa
Energy can be changed from one form to another. Changes in the form of energy are called energy conversions.
Energy Conversion
All forms of energy can be converted into other forms. The sun’s energy through solar cells can be
converted directly into electricity. Green plants convert the sun’s energy
(electromagnetic) into starches and sugars (chemical energy).
Energy conversions
Conceptual understanding
A penny is dropped off the Eiffel tower (ignore air resistance). As it falls, what happens to it’s potential energy? What happens to it’s kinetic energy?
As it falls, its velocity goes up, so its kinetic energy goes up. It also looses height so its potential energy goes down.
However, mechanical energy stays the same ME = KE + PE
Kinetic vs. Potential Energy
At the point of maximum potential energy, the car has minimum kinetic energy.
At the point of maximum kinetic energy, the car has minimum potential energy.
The total mechanical energy stays the same. (Energy cannot be created nor destroyed.
In 1905, Albert Einstein said that mass and energy can be converted into each other.
He showed that if matter is destroyed, energy is created, and if energy is destroyed mass is created. Energy equals the speed of light multiplied by the mass of the object in kilograms.
E = mC2
Einstein’s Take on Law of Conservation of Energy