WORK & POWER
2
3
4
2. How many times would you have to climb the
stairs to burn off your meal of choice?
5
ENERGY
6
7
8
9
10
11
Name _________
Work and Power
Date _________
1. Brutus, a champion weightlifter, raises 260 kg of weights a distance of
2.25 m.
a) How much work is done by Brutus?
b) How much work is done by Brutus holding the weights above his
head?
c) How much work is done by Brutus lowering them back to the
ground?
d) Does Brutus do work if he lets go of the weights and they fall to
the ground?
e) If Brutus completes the lift in 1.9 s, how much power is developed?
12
2. A horizontal force of 805 N is needed to drag a crate across a horizontal
floor with a constant speed. You drag the crate using a rope held at an
angle of 32.
a) What force do you exert on the rope?
b) How much work do you do on the crate when moving 22 m?
c) If you complete the job in 8.0 s, what power is developed?
3. An airplane passenger carries a 223 N suitcase up the stairs, a
displacement of 5.3 m horizontally and 5.6 m vertically.
a) How much work does the passenger do?
b) The same passenger carries the same suitcase back down the same
stairs. How much work does the passenger do now?
13
Reference: Figure B
A 1.0 kg box, initially at rest and a height of 30.0 m, begins sliding down a
frictionless surface. When it reaches the bottom it starts sliding across the horizontal
surface, then has a totally inelastic collision with a 2.0 kg box. They stick together and
begin to slide off together. After leaving this surface, the system is projected horizontally,
from a vertical height of 5.0m.
A) Calculate the speed of the 1.0 kg box at the bottom of the hill (before striking M2).
B) Calculate the speed of the two boxes after they collide.
C) Calculate the speed that the system has when it leaves the surface without
friction and becomes a projectile.
D) Calculate the horizontal range of this projectile.
Figure B:
M1
h = 30m
M1 = 1 kg
M2 = 2 kg
M2
y = 5m
x = ? m
14
WORK, POWER, KINETIC ENERGY & POTENTIAL ENERGY
Description
+ or Work?
Change PE or
KE or Both?
Megan drops the ball and hits an awesome forehand. The racket is
moving horizontally as the strings apply a horizontal force while in
contact with the ball.
A baseball player hits the ball into the outfield bleachers. During
the contact time between ball and bat, the bat is moving at a 10
degree angle to the horizontal.
Rusty Nales pounds a nail into a block of wood. The hammer head is
moving horizontally when it applies force to the nail.
The frictional force between highway and tires pushes backwards
on the tires of a skidding car.
A diver experiences a horizontal reaction force exerted by the
blocks upon her feet at start of the race.
A weightlifter applies a force to lift a barbell above his head at
constant speed.
15
Description of Motion
KE to PE or PE to KE?
Explain.
1.
A ball falls from a height of 2
meters in the absence of air
resistance.
2.
A skier glides from location A
to location B across the
friction free ice.
3.
A baseball is traveling upward
towards a man in the
bleachers.
4.
A bungee chord begins to
exert an upward force upon a
falling bungee jumper.
5.
The spring of a dart gun
exerts a force on a dart as it
is launched from an initial rest
position.
16
Work, Energy, and Power Study Guide
Name:____________
Date:_________
1. Work is done only if the object pushed is ___________ .
2. Potential energy depends upon what three variables?
a. ________________
b. ________________
c. ________________
3. What variables do momentum and kinetic energy have in common?
a. ________________
b. ________________
4. Energy is the ability of an object to make a ____________ in itself
or the environment.
5. List several different types of energy.
a. ________________
b. ________________
c. ________________
d. ________________
6. ____________ is the process of changing the energy of the system.
7. Work is only done if the object is displaced by the__________, in
the same direction as the _________! (same word for both blanks)
8. ___________ is the rate at which work is done.
9. Draw before and after pictures of a collision containing two motion
carts of the same mass. The carts stick together after the collision.
10. Represent the above picture with an equation.
11. The above equation is referred to as the Law of ___________of
_______________.
12. Power is measured in ___________.
13. Energy is measured in ___________.
14. Work done on a system results in ________ energy.
15. Stored energy is referred to as ________ energy.
16. The work-energy theorem states that ________ is equal to
_________.
17
17. Sometimes we say that the energy was lost due to several different
variables. Is the energy truly lost? ____ Where does it go?
____________________________________________________
18. When an object is dropped, it immediately begins to transfer
___________ energy to ___________ energy.
19. A skier starts from rest at the top of a 45-m hill, skies down at 30
degrees into a valley, and continues up a 40-m hill. Both hill heights
are measured from the valley floor. Neglect friction.
a. How fast is the skier moving at the bottom of the first hill?
b. What is the skier’s speed at the top of the next hill?
c. Do your answers depend on the angle of the hill? _____ Why,
Why not? ________________________________________
__________________________________________________
__________________________________________________
20. A 4200-N piano is slid up a 3.5-m plank at a constant speed. The plank
makes an angle of 30 degrees with the horizontal.
a. What is the total height the piano is displaced?
b. Calculate the work done by the person sliding it up the incline.
c. If the worker does the job in 60 seconds, what power do they
generate?
21. A 90-kg rock climber first climbs 45-m up to the top of a quarry,
then descends 85-m from the top to the bottom of the quarry. If the
initial height is the reference level, find the potential energy of the
climber at the top and the bottom. Draw bar graphs for both
situations.
18
Projectiles & Energy Conservation
Pre-Lab
Experimental (Method 1)
Projectile Method
1. Launch car
- measure dx, dy, and h as discussed
in class.
2. Determine ‘t’ using projectile
method (using dy = Vyi t + ½ at2)
3. Using ‘t’, solve for Vx…
Vx = dx / t
4. Solve for Vy…
Vyf2 = Vyi2 + 2ad
5. Solve for Vtot, using vector
analysis… Pythagorean Theorum
6. Using Vtot, and the KE equation
determine the EXPERIMENTAL KE.
7. KE = the energy of the system
Theoretical (Method 2)
Conservation of Energy Method
1. Determine total energy of the
system using the total mass,
gravitational acceleration, and initial
height of the projectile.
2. PE = mgh, where ‘h’ is the total
height of the projectile before the
launch (htot = h + Δy as shown below).
3. Notice that the PE determined
above is converted into the KE the
projectile experiences throughout
the “trip”. (PE = KE)
4. THEORETICAL PE at the top is
ideally equal to KE at the bottom!
h
htot
dy
dx
After solving for the energy of the system using both method 1 & 2,
determine the “energy loss” of the system! (theoretical minus
experimental).
19
Name _______________________ Period _______ Date ___________
CONSERVATION OF ENERGY LABORATORY
Purpose: The purpose of this lab is to apply the law of conservation of energy and
the principle governing projectile motion to determine the amount of energy
lost to friction as a matchbox car rolls down a ramp.
Background and Theory: There are several ways that the motion of objects can be
analyzed. One way is by using kinematic equations and the idea of
independence of horizontal and vertical components of the motion. Another
way is by using the Law of Conservation of Mechanical Energy. In this
laboratory, both methods will be used in determining the mechanical energy
“lost” due to the dissipative force of friction. It is important to remember
that the energy is not actually gone; rather it is converted into some other
form.
When using the Law of Conservation of Mechanical Energy, conditions
are assumed to be ideal, with no dissipative forces involved. Realistically,
however, as a car rolls down a ramp, the force of friction does lead to a loss
of mechanical energy. In calculating the mechanical energy at the bottom of
the ramp, the value will be higher than it should be, since the force of
friction has not been considered. By finding the actual velocity at the
bottom of the ramp using projectile motion methods, a more accurate value
of the energy can be obtained. The difference in the energy values of each
method gives a good indication of how much energy was “lost” to friction.
Materials: matchbox car, ramp, meter stick, tape
Procedure:
1. Set up the apparatus as demonstrated.
2. Measure the height (h) to the top of the track in reference to the table
top.
3. Measure the height of the table (Δdy).
4. Set your matchbox car at the top of the ramp, launch it, and note its
approximate landing position on the floor.
5. Place a piece of carbon paper on top of a piece of notebook paper on the
floor where the car landed.
6. Measure the horizontal distance
h
h
(Δx) from the point of launch at
the end of the ramp to the landing
htot
location of the car.
dy
20
dx
Data and Calculations:
Table 1: Raw Data
Trial
dy (m)
h (m)
htot (m)
1
2
3
“
“
“
“
“
“
dx (m)
m (kg)
“
“
Table 2: Calculated data
Method 1
Trial
1
2
3
Ave
Method 2 (PE = mgh = KE)
(projectile motion)
IN PRACTICE
Vx
(m/s)
IN THEORY
Vy
(m/s)
“
“
“
Vtot (m/s) KE (1)
(J)
PE (J)
KE (J)
“
“
0
0
0
0
Energy Loss
(J)
*Show one sample calculation for each variable of table 2 in lab notebook.
Analysis:
1. In which method of calculating kinetic energy should you reach a result
that is closer to the “actual” kinetic energy of the car? Why?
2. In which method of calculating kinetic energy will the answer be true only
if there was no friction or outside forces acting on the system?
3. In this lab, you calculated an energy loss. Where did this energy go? In
what form was it lost?
4. Explain the main idea behind this lab. Specifically: Why are we able to
subtract the kinetic energies from each method to find the energy lost to
friction?
21
Energy of a Tossed Ball
When a juggler tosses a bean ball straight upward, the ball slows down until it reaches the
top of its path and then speeds up on its way back down. In terms of energy, when the
ball is released it has kinetic energy, KE. As it rises during its free-fall phase it slows
down, loses kinetic energy, and gains gravitational potential energy, PE. As it starts
down, still in free fall, the stored gravitational potential energy is converted back into
kinetic energy as the object falls.
If there is no work done by frictional forces, the total energy will remain constant. In this
experiment, we will see if this works out for the toss of a ball.
Motion Detector
No basket necessary, do
not let the ball hit the
motion detector
In this experiment, we will study these energy changes using a Motion Detector.
OBJECTIVES

Measure the change in the kinetic and potential energies as a ball moves in free fall.
 See how the total energy of the ball changes during free fall.
MATERIALS
computer
Vernier computer interface
Logger Pro
Vernier Motion Detector
volleyball, basketball, or other similar,
fairly heavy ball
PRELIMINARY QUESTIONS
For each question, consider the free-fall portion of the motion of a ball tossed straight
upward, starting just as the ball is released to just before it is caught. Assume that there is
very little air resistance.
1. What form or forms of energy does the ball have while momentarily at rest at the top
of the path?
22
2. What form or forms of energy does the ball have while in motion near the bottom of
the path?
3. Sketch a graph of velocity vs. time for the ball.
4. Sketch a graph of kinetic energy vs. time for the ball.
5. Sketch a graph of potential energy vs. time for the ball.
6. If there are no frictional forces acting on the ball, how is the change in the ball’s
potential energy related to the change in kinetic energy?
PROCEDURE
1. Measure and record the mass of the ball you plan to use in this experiment.
2. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface. Place the
Motion Detector on the floor and protect it by placing a wire basket over it.
3. Open the file “16 Energy of a Tossed Ball” from the Physics with Vernier folder.
4. Hold the ball directly above and about 1.0 m from the Motion Detector. In this step,
you will toss the ball straight upward above the Motion Detector and let it fall back
toward the Motion Detector. Have your partner click
to begin data collection.
Toss the ball straight up after you hear the Motion Detector begin to click. Use two
hands. Be sure to pull your hands away from the ball after it starts moving so they are
not picked up by the Motion Detector. Throw the ball so it reaches maximum height
of about 1.5 m above the Motion Detector. Verify that the position vs. time graph
corresponding to the free-fall motion is parabolic in shape, without spikes or flat
regions, before you continue. This step may require some practice. If necessary,
repeat the toss, until you get a good graph. When you have good data on the screen,
proceed to the Analysis section.
DATA TABLE
Mass of the ball
Position
Time
(s)
Height
(m)
(kg)
Velocity
(m/s)
PE
(J)
KE
(J)
TE
(J)
After release
Top of path
Before catch
23
ANALYSIS
1. Click on the Examine tool, , and move the mouse across the position or velocity
graphs of the motion of the ball to answer these questions.
a. Identify the portion of each graph where the ball had just left your hands and was
in free fall. Determine the height and velocity of the ball at this time. Enter your
values in your data table.
b. Identify the point on each graph where the ball was at the top of its path.
Determine the time, height, and velocity of the ball at this point. Enter your values
in your data table.
c. Find a time where the ball was moving downward, but a short time before it was
caught. Measure and record the height and velocity of the ball at that time.
d. For each of the three points in your data table, calculate the Potential Energy (PE),
Kinetic Energy (KE), and Total Energy (TE). Use the position of the Motion
Detector as the zero of your gravitational potential energy.
2. How well does this part of the experiment show conservation of energy? Explain.
3. Logger Pro can graph the ball’s kinetic energy according to KE = ½ mv2 if you
supply the ball’s mass. To do this, choose Column Options Kinetic Energy from the
Data menu. Click the Column Definition tab.You will see a dialog box containing an
approximate formula for calculating the KE of the ball. Edit the formula to reflect the
mass of the ball and click
.
4. Logger Pro can also calculate the ball’s potential energy according to PE = mgh.
Here m is the mass of the ball, g the free-fall acceleration, and h is the vertical height
of the ball measured from the position of the Motion Detector. As before, you will
need to supply the mass of the ball. To do this, choose Column Options Potential
Energy from the Data menu. Click the Column Definition tab. You will see a dialog
box containing an approximate formula for calculating the PE of the ball. Edit the
formula to reflect the mass of the ball and click
.
5. Go to the next page by clicking on the Next Page button,
.
6. Inspect your kinetic energy vs. time graph for the toss of the ball. Explain its shape.
7. Inspect your potential energy vs. time graph for the free-fall flight of the ball. Explain
its shape.
8. Record the two energy graphs by printing or sketching.
9. Compare your energy graphs predictions (from the Preliminary Questions) to the real
data for the ball toss.
10. Logger Pro will also calculate Total Energy, the sum of KE and PE, for plotting.
Record the graph by printing or sketching.
24
11. What do you conclude from this graph about the total energy of the ball as it moved
up and down in free fall? Does the total energy remain constant?
12. Should the total energy remain constant? Why?
13. If it does not, what sources of extra energy are there or where could the missing
energy have gone?
THOUGHT EXPERIMENTS (DO NOT PERFORM, JUST PREDICT)
1. What would change in this experiment if you used a very light ball, like a beach ball?
2. What would happen to your experimental results if you entered the wrong mass for
the ball in this experiment?
3. Predict what would happen in a similar experiment using a bouncing ball. To do this,
you would mount the Motion Detector high and pointed downward so it can follow
the ball through several bounces.
25
STUDY GUIDE II
Part I - Mechanical Energy
W  F d
PE  mgh
KE 
1
mv 2
2
W  KE
1. Identical twins Pat and Chris are painting a house. Pat is standing on the
scaffolding 5 meters above the ground. Chris is standing on the
scaffolding 5 meters above Pat. Who has more potential energy?
Explain.
2. Jared and Clay are climbing the stairs. Jared gets tired and stops
halfway to the fourth floor. Clay makes it to the fourth floor without a
problem. If Jared is twice as heavy as Clay, who has more potential
energy? Explain.
3. A person weighing 630 N climbs up a ladder to a height of 5 meters. How
much work does the person do? Determine the increase in the potential
energy of the person from the ground to this height. Where does the
energy come from to cause this increase in PE?
4. Calculate the kinetic energy of a 750 kg car moving at 13.9 m/s. What is
the kinetic energy of the car if the speed is doubled? How much work
must be done to double the speed?
5. A rifle can shoot a 4.2 g bullet at a speed of 965 m/s. Find the kinetic
energy of the bullet. What work is done on the bullet if it starts from
rest? If the work is done over a distance of 75 cm, determine the
average force acting on the bullet.
26
Part II – Problem Solving with Conservation of Energy
Eo  E f
PE  mgh
KE 
1
mv 2
2
1. A large chunk of ice with mass 15 kg falls from a roof 8 meters above the
ground. Find the kinetic energy of the ice when it reaches the ground.
What is the speed of the ice when it reaches the ground?
2. A bike rider approaches a hill with a speed of 8.5 m/s.
The total mass of the bike and the rider is 85 kg. Find
the kinetic energy of the bike and rider. If the rider
coasts up the hill, calculate the height at which the
bike will come to a stop. (Assume there is no friction.)
How would your answer vary if the mass of the bike
and rider were doubled?
3. A 2 kg rocket is launched straight up into the air with a speed that allows
it to reach a height of 100 meters, even though air resistance performs
800 J of work on the rocket. Determine the launch speed of the rocket.
How high would the rocket travel if air resistance is ignored?
27
28
4. Calculate the potential energy, kinetic energy, mechanical energy, velocity, and height of the skater at
the various locations.
Part III – Problem Solving with Conservation of Energy
Eo  E f
o   f
PE  mgh
KE 

1
mv 2
2

  mv
1. A 20 kg rock is on the edge of a 100 meter cliff. Calculate the potential
energy of the rock. If the rock falls off the cliff, what is its kinetic
energy just before striking the ground? What speed does the rock have
as it strikes the ground?
2. A physics book is dropped 4.5 meters. What speed does the book have
just before it hits the ground?
3. From what height would a compact car have to be dropped to have the
same kinetic energy that is has when being driven at 100 km/hr?
4. A 70 kg high jumper leaves the ground with a speed of 6 m/s. How high
can he jump?
5. Just before striking the ground, a 900 kg Smart Bomb has 88.2 MJ of
kinetic energy. If air resistance is ignored, determine the height from
which the Smart Bomb was dropped. Determine the drop height if air
resistance performs 8.82 MJ of work against the bomb as it falls
towards its target.
6. A 74 kg student, starting from rest, slides down an 11.8 meter high water
slide. On the way down, friction does 5600 J of work on him. How fast is
he going at the bottom of the slide?
7. Block A with a mass of 12 kg moving at 2.4 m/s makes a perfectly elastic
head-on collision with block B, mass 36 kg, at rest. Find the velocities of
the two blocks after the collision. Assume all motion is in one dimension.
29
30
8. Calculate the potential energy, kinetic energy, mechanical energy, velocity, and height of the ball at the
various locations.
Part IV - Chapter Review
W  F d
PE  mgh
Eo  E f
W  KE
KE 
1
mv 2
2
1. Jamie lifts her toys into her tree house using a homemade elevator. The
elevator has a mass of 2.5 kg and the tree house is 8 meters above the
ground. How much work does Jamie do when lifting 5 kg of toys into the
house? Determine the power used to lift the toys in 5 sec.
2. Mike pulls a sled across level snow with a force of 225 N using a rope
that is angled at 35. Determine the work done if he pulls the sled 65.3
meters.
3. A 2 kg textbook is lifted from the floor to a shelf 2.1 meters above the
floor. Determine the book’s potential energy relative to the floor. What
is the book’s potential energy relative to the head of a 1.65 meter tall
person?
4. A shot-putter heaves a 7.26 kg shot with a velocity of 7.5 m/s.
Determine the kinetic energy of the shot. How much work was done on
the shot to give it its kinetic energy?
5. Calculate the kinetic energy of a 750 kg compact car moving at 100
km/hr. How much work must be done to slow the car down to 50 km/hr?
6. Determine the mechanical energy of a 450 kg roller coaster moving at 30
m/s at the bottom of the first dip which is 15 meters above the ground.
7. Julie has a mass of 49 kg. What is her potential energy when standing on
the 6 meter diving board? (She is 6 meters above the water.) Julie
jumps off the diving board. What is her kinetic energy right before she
hits the water? How fast does Julie hit the water?
8. An unfortunate skydiver’s parachute fails to open. If the diver hits the
ground going 300 m/s, determine the height from which the ill-fated
jump was make.
31
32
9. Calculate the potential, kinetic, and mechanical energies, velocity, work, and power of the ball at the
various locations.
Where did the term horsepower originate?
The term horsepower came from Scottish inventor James
Watt. The value for a unit of horsepower was determined
after Watt performed several experiments on horses pulling
coal. He originally determined that the average horse was able
to pull 22,000 foot-pounds every one minute. In other words,
a horsepower was defined as the amount of power exerted to
move 22,000 pounds of coal by one foot in one minute. Watt
was not happy with his figure because he felt it was too low;
he thought the average horse was more powerful than his
original calculations and experiment indicated, so after
extensive study of horses, he increased the value of a
horsepower to 33,000 foot-pounds per minute. (1 HP = 746 W)
What countries are the largest consumers of energy?
The United States consumes over 28% more energy than it
produces. That accounts for nearly a quarter of the energy
consumed throughout the entire world, while the population of
the United States accounts for only 5% of the world’s
population.
Rank
1
2
3
4
5
6
7
8
9
10
Country
United States
China
Russia
Japan
Germany
Canada
India
United Kingdom
France
Italy
33
What are the average yearly costs of some general home appliances?
Home climate control and appliances account for approximately
one third of the energy consumption in the United States. The
average cost for energy is approximately $0.12 per KwH (kilowatthour), but varies throughout the country. The following is a listing
of home appliances, their typical usage, and the cost for one full
year.
Appliance
Television
Energy (KwK) Annual Cost @ $0.12 / Kw
1000
$120
1000
150
1000
1200
2000
5000
1500
$120
$18
$120
$152
$240
$600
$180
(8 hours per day)
Stove with Oven
Washer
Dryer
Refrigerator
Frost-free Refrigerator
Hot-water Heater
Window Air-conditioner
(if used year ‘round)
34