Physics: ENERGY!
“I HAVE THE POWER!” – He-Man
Name__________________________
1 2 3 4 5 6 7 8
Day
Schedule
Homework
1
Definitions of Energy
Worksheet 1: Energy Bar Graphs
2
Whiteboard WS:1
Working and Energy Transfers
Worksheet 2: Energy Transfers
3
Whiteboard WS:2
Hooke’s Law Prelab
Begin Hooke’s Law Lab Report
4
Hooke’s Law Lab
Lab Results
Worksheet 3: Hooke’s Law and
Spring Potential
5
Whiteboard WS:3
Gravitational Potential Energy
Worksheet 4: GPE, Work, and
Spring Potential
6
Whiteboard WS:4
Begin Energy Transfers Lab
FINISH LAB REPORT FOR HOOKE’S
LAW
Finish Transfers Lab Sheet
7
Finish Energy Transfers Lab
8
Lab Results
Worksheet 5: Kinetic Energy
9
Whiteboard WS:6
Energy Conservation Problems
Begin Worksheet 6: Conservation
of Energy Problems
10
Conservation of Energy
Finish WS:6
11
Whiteboard WS:6
Power
Worksheet 7: Power
12
Whiteboard WS7
13
Review
14
TEST
15
ROLLERCOASTERS
16
ROLLERCOASTERS
Review Guide
Reading
Physics Classroom – Work,
Energy, and Power – Lesson
2c
Physics Classroom – Work,
Energy, and Power – Lesson
1b
Physics Classroom – Work,
Energy, and Power – Lesson
1a
Physics Classroom – Work,
Energy, and Power – Lesson
1c
Physics Classroom – Work,
Energy, and Power – Lesson
1b,c,d
Physics Classroom – Work,
Energy, and Power – Lesson
1e
BIG IDEAS
Conservation
Law
Theorem
1
Energy
Momentum
Energy is always constant, therefore…
Momentum is always constant, therefore…
Total Energy Before = Total Energy After
Total Momentum Before = Total Momentum After
KEi + PEi + Work = KEf + PEf + Heat
m1v1i +m2v2i = m1v1f + m2v2f
Work-Energy Theorem
Impulse-Momentum Theorem
Work = ∆Energy
Impulse = ∆Momentum
Fd = ∆(energy)
Ft = ∆(mv)
Energy Types:
Kinetic (Motion) – 1/2mv2
Gravitational Potential – mgh
Spring Potential – 1/2kx2
Sound, Light, Nuclear, etc…
Work = Fdcosθ – If force is perpendicular to distance, that force does NO WORK!
Power = Energy Converted/time = Work/time
1
These ideas are SO BIG that they get their own
BIG FONT.
Physics: Energy
Worksheet 1: Energy Bar Graphs
Name__________________________
1 2 3 4 5 6 7 8
Use bar graphs to analyze the energy changes in each situation given.
• Designate your choice of system with a dotted line,
• Carefully label the graphs to correspond with the positions of the objects given. (A, B, C, etc.)
• The graphs should be accurately labeled with the type(s) of energy involved.
1. A ball is held above the ground, and then is dropped so it falls straight down.
(The last picture is the moment BEFORE the ball hits the ground.)
2. A wind-up toy is wound up, then "walks" across a table and comes to a stop.
3. A baseball is thrown up in the air and then falls back down. Draw a graph for each position shown.
4. A ball rolls to a stop on the floor.
©Modeling Workshop Project 2006
1
5. A superball is dropped and bounces up and down. Draw a graph for each position of the ball shown.
Why does the ball not bounce as high each time? Where did the energy "go"?
6. An object rests on a coiled spring, and is then launched upwards.
7. A piece of clay is dropped to the floor.
8. A truck is driven at constant speed down the street.
©Modeling Workshop Project 2006
2
Physics: Energy
Worksheet 2: Work and Changing Energy
Name______________________________
1 2 3 4 5 6 7 8
For each situation below, make sure you pay attention to what the system is defined as!
1. A car on a roller coaster track, launched by a huge spring, makes it to the top of the loop. The system is
the car and the spring! Assume no friction.
2. The same situation as #1, except now the system is only the car. There is still no friction!
3. The same car is launched by the spring, but it is only half way up the loop. There is no friction, and the
system is the car and the spring.
4. A moving car, moving up a hill, coasts to a stop up. The system is the car, and there is no friction!
©Modeling Workshop Project 2006
1
5. A person pushes a stalled car to get it to the service station. The system is the car only! The car starts
from rest.
6. A load of bricks, resting on a compressed spring, is launched into the air. The system is the load of bricks
and the spring!
7. A crate, starting at rest, is propelled up a hill by a tightly coiled spring. The system is only the crate, and
there is no friction!
8. Now, the system includes the spring.
©Modeling Workshop Project 2006
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8. A bungee jumper falls off the platform and reaches the limit of stretch of the cord. The system is the
person and the cord!
9. Superman, stopping a speeding locomotive, is pushed backwards a few meters in the process. The system
is only the locomotive!
©Modeling Workshop Project 2006
3
The Squirrel Workout
Physics 432
Name ______________________
1 2 3 4 5 6 7 8
Nutty the squirrel loves to work out. For the following
exercises, determine how much work Nutty does.
1) As a warm-up, Nutty takes his heavy 200N weights and pushes them 35m across the floor at a constant speed. If he is
pushing with 50 N of force, how much work did he do?
2) Our Squirrelly companion now takes out his barbells and lifts a 15N weight .3 meters over his head. How much work
did he do in this situation?
3) The now sweaty squirrel holds his 15N weight over his head. While keeping the weight above his head, he runs a
100m dash in 22 seconds. How much work did he do?
4) Returning back, Nutty starts his stair workout. If his mass is 1kg, and each flight of stairs is 4 meters, then how much
work does he do in each situation:
a- run up two flights of stairs.
b- run up three flights, then back down one.
c- run up three flights of stairs.
5) A very tired Squirrel of 1kg mass begins to do pushups to elevate himself .05m. How many pushups should he do to
accomplish 5.0 J of work?
6) After his finished workout, Nutty considers all of the work that he has done.
Did he do positive or negative work while he was exercising? ______________________
Did his 15N barbell do positive or negative work? _______________________________
Physics: Energy
Worksheet 3: Hooke’s Law
Name__________________________
1 2 3 4 5 6 7 8
Suppose in the lab one group found that F=1000. mN (x ) . Draw a graph of force vs. displacement in the
space below. (Hint: make the maximum displacement 0.25 m.)
1. How much energy is stored in the spring when it is stretched
from x = 0 m to x = 0.10 m?
2. How much energy is stored in the spring when it is stretched
from x = 0.15 m to x = 0.25 m?
The graph below was made from data collected during an
investigation of the relationship between the amount two different springs stretched, when different forces
were applied.
36.0
3. For each spring determine the spring constant.
Data Set 1
Data Set 2
32.0
28.0
24.0
4. For each spring, compare
a. the amount of force required to stretch the spring 3.0 m.
Force (N)
20.0
16.0
12.0
8.00
b. the Eel stored in each spring when stretched 3.0 m.
4.00
0.00
0.00
2.00
4.00
x (m)
©Modeling Workshop Project 2006
6.00
8.00
1
5. Determine the amount that spring 2 needs to be stretched in order to store 24 joules of energy.
6. The spring below has a spring constant of 10 N/m.
a. If the block is pulled 0.30 m horizontally to the right, and held motionless, what force does the spring exert
on the block?
b. Sketch a force diagram for the mass as you hold it still. (Assume a frictionless surface.)
c. Do a bar graph analysis for this situation when the spring is stretched and then allowed to return back
to equilibrium. Assume your system includes the spring, box, and tabletop. There IS friction between
the box and the tabletop. You should have three pictures: (1) stretched spring, (2) box moving back
to equilibrium, and (3) box is back at the start.
©Modeling Workshop Project 2006
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Physics: Energy
Worksheet 4: GPE, Work, and Spring Potential
Part I: Basic Practice
1. An 8 kg bowling ball is held 5 m above the
ground. How much gravitational potential
energy does the ball store?
2. A 40 kg dog has 400 J of gravitational
potential energy. How high above the
ground is the dog?
3. Lassie, the 20-kg astrodog, is taken to a
new planet. On this planet she has 450 J of
PE when she is 8 meters above the surface
of the planet. What is the acceleration due
to gravity on this planet?
4. A briefcase full of mysterious light stores
235 J of gravitational potential energy. If
the briefcase is being held 4 m off the
ground, what is the mass of the briefcase?
(This is on earth!)
Name__________________________
1 2 3 4 5 6 7 8
5. An archer pulls back a 0.25 kg arrow 0.6
meters. If the spring constant of the bow is
100 N/m, how much spring potential
energy does the arrow have?
6. SPOILER ALERT! Katniss Everdeen pulls her
bow back to take a shot at a President
Snow. If her bow has a spring constant of
95 N/m, and she pulls back the bow 0.5 m,
how much energy does the 0.15 kg arrow
store?
7. A trampoline spring is stretched a distance
of 0.56 m. The spring has a constant of 200
N/m. How much energy is stored in the
spring?
8. A sling shot is stretched to 0.25 m. If the
spring constant of the sling shot is 80 N/m,
how much energy does the slingshot store?
Part II: Working to Add Energy
9. If 25 J of work are done to lift a gold bar into the air, how much energy does the bar now have?
10. A rubber band is stretched from 0.10 m to 0.12 m. The rubber band has a spring constant of 12 N/m.
How much work was done to stretch the rubber band?
11. A spring launches a box of miniature horses 10 m into the air. The mass of the box is 250 kg.
a. How much gravitational potential energy does the box of horses have when it is at its peak?
b. Where did the box of horses get that energy?
c. How much work was done by the spring? Assume the box started from ground level.
d. If the spring constant of the spring is 2300 N/m, how far was the spring compressed?
12. A crate of crapes (m = 12 kg) is lifted 12 m into the air. How much work was done on the crate?
13. Hawkeye uses a bow with a constant of 1,100 N/m. He loads the bow with an arrow of mass 0.50 kg,
and draws the bow back 0.85 m.
a. How much energy does the bow store when it is drawn back?
b. How much of that energy is given to the arrow?
c. If he shoots the arrow straight up into the air, how high will it travel?
Physics: Energy
Energy Transfers Lab
Name__________________________
1 2 3 4 5 6 7 8
Be sure to follow the directions carefully and answer all the questions!
1. Gather the materials you need, and build the lab
setup shown to the right.
2. What is the spring constant, k, of your spring? This information was given to you before you started
the lab!
3. What equation will you use to find the energy stored in the spring?
4. Describe the procedure you will use to determine the energy stored in the spring.
5. Make sure the motion detector is connected properly, and make sure you can see the velocity of the
car on the graph and in your data table.
6. Describe how you will use the motion detector to find the maximum velocity of the cart.
7. Fill in the data table below with your values for energy stored in the spring and the maximum
velocity of the car.
Energy Stored (J)
Maximum Velocity (m/s)
8. Using Logger Pro or Excel, create a graph of Energy Stored vs. Maximum Velocity. Be sure to include
labels and units on each axis.
9. What is the relationship between energy stored and maximum velocity?
10. The unit for your slope reduces to a simple unit we have been using all year. What is it? (Hint: 1 J = 1
Nm and 1 N = 1 kg m/s2)
Physics: Energy
Kinetic Energy and Work
Part I: Basic Calculations
1. How much kinetic energy does an 8-kg
bowling ball have if it moves at 6 m/s?
2. A taco strikes a wall with a velocity of 8.5
m/s and a kinetic energy of 40-J, what is
the mass of the taco?
3. If a 4-kg cat flung from a trebuchet has 60J of kinetic energy, how fast is the cat
moving?
Name__________________________
1 2 3 4 5 6 7 8
5. A 25 N force is applied to a cart for a
distance of 6.2 m. How much work was
done on the cart?
6. In order to lift a crate of waffles 2.5 m, JJ
must do 35 J of work. How much force
would that require?
7. Luke Skywalker uses “the Force” to pull his
lightsaber toward him from a distance of
2.5 m away. His standard lightsaber has a
mass of 1.2 kg, and Luke must exert 35 N
of force to pull the lightsaber. How much
work does he do?
4. A 1500-kg truck changes its velocity from
15m/s to 30m/s. What is the increase in
KE of the truck?
8. Yoda lifts Luke’s X-Wing a distance of 1.4
m using a force of 49442 N. How much
work does Yoda do?
Part II: Relationships
9. A box (m = 48 kg) is pushed with a force of 151 N for a distance of 62 m.
a. How much work is done on the box?
c. What is the velocity of the box after
it is pushed?
b. What is the change in energy of the
box?
10. Hawkeye again draws back his 1,100 N/m bow to a distance of 0.80 m. This time, he loads it with a
trick arrow that has a mass of 0.60 kg.
a. How much energy does the bow store when it is drawn back?
b. How much of that energy is transferred to the arrow?
c. What is the velocity of the arrow right after it leaves the bow?
11. A baseball (m = 2 kg) is thrown with a velocity of 40.2 m/s.
a. What is the kinetic energy of the baseball?
b. How much work must be done in order to stop the baseball?
c. What force must be exerted by the catcher’s mitt to stop the ball in a distance of 0.25 m?
12. A car is moving with a velocity of 35 m/s. The car has 1225000 J of kinetic energy.
a. What is the mass of the car?
b. If the mass of the car is increased, what will happen to the velocity of the car?
c. A giant boulder falls onto the car, but everyone in the car is fine. If the boulder has the same
mass as the car, what is the new velocity of the car/boulder combo?
Physics: Energy
Worksheet 6: Conservation of Energy
Part I: Fill out the chart
KE = (½) mv2
Name:_______________________________
1 2
3 4 5
6 7 8
PEg = mgh
PEk =(1/2)kx2
Ebef = Edur = Eaft
PEg
elastic potential energy
Is there a stretched or compressed spring?
½ mv2
Part II: Questions
Read each of the following statements and identify them as having to do with kinetic energy (KE), gravitational
potential energy (PEg), elastic potential energy (PEk) or all three (A3).
1) If an object is at rest, it certainly does NOT possess this form of energy.
2) Depends upon object mass and object height.
3) The energy an object possesses due to its motion.
4) The energy that involves a variable that has units of N/m.
5) The amount is expressed using the unit joule (abbreviated J).
6) The energy stored in an object due to its position (or height).
7) The energy that determines how much work the object can do.
8) The energy that depends on the “stiffness” of stretchy object.
9) The amount depends upon the arbitrarily assigned zero level.
10) Depends upon object mass and object speed.
11) The energy that depends on how far an object is stretched.
12) If an object is at rest on the ground (zero height), it certainly does NOT possess this form of energy.
Part III: Write the equation and give a real life example of the situation. The first has been done for you.
13) An object starts with elastic
PE and ends with KE.
1/2kx2 = 1/2mv2
arrow pulled back then
14) An objects starts with kinetic
energy and ends with
gravitational potential energy.
15) An objects starts with kinetic
energy and gravitational PE,
then ends with kinetic energy.
16) An object starts with
gravitational PE and ends with
kinetic energy.
17) An object begins with
gravitational PE some of which
turns into kinetic energy.
18) An object starts with elastic
PE some of which then turns
into KE, gravitational PE.
shot
Part IV: Problems
19) A ball slides down the frictionless track shown below. The ball has no velocity at position F.
G
C
F
E
A
B
a) To what point does the ball rise on the opposite incline?
b) At what point(s) in the diagram is the speed at a maximum?
c) At what point(s) is the kinetic energy at a maximum?
d) At what point(s) is the speed zero?
e) At what point(s) is the potential energy at a minimum?
f) At what point(s) is the potential energy at a maximum?
g) At what point(s) is the momentum at a maximum?
20) A pendulum is pulled sideways so that it is raised a vertical distance of 2 m above its resting position. Find the
maximum speed the pendulum reaches after being released.
2m
21) An archer pulls back on a 0.25 kg arrow 1.5 m using bow. He then shoots the arrow and it leaves the bow traveling
at 120 m/s, what is the spring constant of the bow?
22) A man standing on top of a 30 m tall building drops a brick. Determine the speed of the brick just before it hits
the ground.
23) How high will a 60kg girl go if she stretches a trampoline (100 N/m) 1.4 m?
24) The frictionless car below is moving at 4 m/s at position A (50 m above ground level). It has a mass of 1000 kg and
is rolling along the hills in neutral. Point B is at ground level.
A
a) What is the total energy of the car at point A?
B
h=0
b) What is the total energy of the car at point B?
c) How fast will the car be moving when it reaches position B (at ground level)?
d) What is the maximum height above the ground that the car can reach on the right side?
25) At point “A” on the hill, there is a skier at rest.
A
D
12 m
C
4m
8m
B
a) Find the skier’s maximum speed. Where on the hill does she achieve this speed?
b) How far vertically up the other hill will the skier be able to go?
c) How fast will the skier be moving at point C?
d) How fast will the skier be moving at point D?
26) A water balloon is shot upwards with a velocity of 55 m/s. How high does it travel?
27) A man standing on top of a 30 m tall building throws a brick downwards with a velocity of 12 m/s. Determine the
speed of the brick just before it hits the ground.
28) A 80 kg kid seeking attention jumps off of a garage roof onto a trampoline. If he is traveling at 8 m/s just before
he begins to stretch the 120 N/m trampoline, how far will the trampoline stretch before it flings him upwards?
29) An archer pulls back on a 0.2 kg arrow 1.0 m using a 60 N/m bow. He then shoots the arrow. What is the velocity
of the arrow one third of the way out of the bow?
2(10m/s2)(5m) + ½(2m/s)2
Part V: Backwards Problems
1) Draw a picture of the work shown, and 2) give the equation being solved
30)
31)
20 /
0.8
.
/
.
/
/
32) 10.1 /
33) 448 /
2 10 / ^2 5
2 2
10 / ^2 3
.5
1/2 2 / ^2
1/2 2
^2
92 / ^2
Physics: Energy
Worksheet 7: Power!
“By the power of Grayskull…”
Name__________________________
1 2 3 4 5 6 7 8
“I have the power!” – He-Man
1. He-Man needs to do 350 J of work to lift Skeletor above his head. If He-Man can do this in 1.4 s, how
much power does he exert?
2. Battle Cat can push a box for 3.5 s while exerting a force of 250 N. If the box moves 2.5 m, how
much power does Battle Cat exert?
3. Orko (m = 25 kg) runs up a hill to a height of 5 m. If his power is 150 Watts, how much time did it
take him to run up the hill?
4. He-Man can lift a box 1.2 m straight into the air in a time of 0.56 s. If his power is 1060 Watts, what
is the mass of the box?
5. The evil Skeletor (m = 45 kg) decides he needs to put some muscles on his bones. If he does one
pushup (of height 0.75 m) in a time of 2 s, how much power did he exert?
6. If Skeletor does 30 pushups in 20 seconds, how much power did he exert?
A weightlifter is using his tremendous muscles to lift a barbell, exerting 20 watts of power in the process. For
each question, indicate how the power will change.
7) If the weightlifter now lifts the barbell twice as high in the same time period, how will his power change?
Factor changed
New Power
8) If the weightlifter lifts the weight in twice as much time, how will his power change?
Factor changed
New Power
9) If the weight is changed to become 4 times as massive, how will his power change?
Factor changed
New Power
10) If the weightlifter uses a weight that is ½ as massive, and lifts it in ½ the time, how will his power
change?
Factor changed
New Power
11) If the weightlifter lifts the weight 3 times the original height in ¼ the original time, how will his power
change?
Factor changed
New Power
12) List two ways to increase the weightlifter’s power by 12 times (power = 240 watts).