Study Guide - Work, Power, Energy, & Conservation
Vocabulary (including the SI units of quantities)
Work Power Watt Joule Potential Energy Kinetic Energy Mechanical Energy Work-Energy Theorem Law of Conservation of Energy Problem Solving:
Examples of Work & Power Problems

An electric motor lifts a 2000 kg elevator a distance of 18 m in 40 s.
1. How much work is done?
W=Fd W=(2000x9.8)(18)
W= 352,800J
OR W=Fd(cosΘ) W=(2000x9.8)(18)(cos0)
W= 352,800J
Cos(Θ) is in the work equation only if a force is at an angle from the motion. If it is at an angle, only part of the force does the
work – the part of the force that is in the same direction as the motion. For our purposes, we always had the force and motion in
the same direction which is a zero degree angle. The cosine of zero is one so it is not necessary to include that in the calculation
or equation.
2. What is the power of the motor? P=W/t P = 3528000/40 P=8820W
3. If the mass and distance are doubled, what happens to the amount of work done? Quadruples
a.
What work is done to accelerate a 1500 kg truck from 25 m/s to 35 m/s?
Work done = change in kinetic energy. So Work = KEfinal - KEinitial
b.
W = ½ (1500) 352 - ½ (1500) 252
W = 450,000 J
What work is done in dragging a 3.5 kg block with 2.3 N of force at a 250 angle along a lab table for 1.5 m?
W=Fd(cosΘ) W = 2.3 x 1.5 cos(25) W = 3.13J
Not all the force was used to do work – only the horizontal component of
the force helped to move the block. The cos25 helps to include only the horizontal component of the force in the calcuation.
2.


Examples of PE, KE and Conservation of Energy Problems
A 60 kg shell is shot from a cannon to a height of 400 m.
1. What is the potential energy of the shell at its highest point?
PE = mgh
PE = 60x9.8x400
PE = 235,200J
2.
What is the kinetic energy of the shell as it falls from its highest point to a height of 150m?
Highest point (400m) = 150m height
PE + KE = PE + KE
mgh + 0 = mgh + KE
60 x9.8 x 400 = 60 x9.8 x 150 + KE
235,200 =88200 + KE
KE = 147,000J
3.
What is its final velocity just before striking the ground? (all potential energy is now converted to kinetic)
KE = ½ mv2
235200 = ½ x 60 v2
2 x 235200/ 60 = v2
Square root both sides
v = 88.5m/s
A 75 kg sled rider on a 30 kg sled is poised at the top of a snow covered hill. The hill is 100 m long and 30 m high.
1. What is the rider's speed at the bottom of the hill?
Top of hill = bottom of hill
PE + KE = PE + KE
mgh + 0 = 0 + ½ mv2
9.8 x 30 = ½ v2
v = 24.2 m/s
2. What is the GPE of the rider and sled at the top of the first hill?
PE =mgh PE = 105x9.8x30 PE= 30,870J
3.
What is the rider's speed at the bottom of the first hill?
See #1 DUPLICATE
4. What is the rider's GPE at the top of the second hill? Assume 2nd hill is 22 meters tall.
PE =mgh PE = 105x9.8x22 PE = 22,628J
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5.
What is the change in GPE from the top of the first hill to the top of the second hill?
PE = 30870 – 22628 PE = 8232
6.
What is the rider's speed at the top of the 2nd hill that is 22 m high?
Bottom of first hill = top of 2nd hill (there are other equally good ways to do this problem)
PE + KE = PE + KE
0 + ½ mv2 = mgh + ½ mv2
½ (24.2)2 = 9.8 x 22 + ½ v2
v = 12.4 m/s (or 12.5 m/s if you use a different method  top of 1st hill = top of 2nd hill)
Concepts
1. In physics, work is defined as
A) force times time.
B) force divided by distance.
C) distance divided by time.
D) force divided by time.
E) force. cos  distance.
2. In which of the following systems is there a decrease in gravitational potential energy?
A) a boy stretches a spring
B) a girl jumps down from a bed
C) a crate rests at the bottom of an inclined plane
D) a car is driven up a steep hill
E) water is forced upward through a pipe
3. Which of the following is an example of an object that possesses kinetic energy?
A) a drum of diesel fuel on a parked truck
B) a stationary pendulum
C) an orbiting satellite
D) a car parked at the top of a hill
E) a boulder resting at the bottom of a cliff
4. If Nellie Newton pushes an object with twice the force for twice the distance, she does
A) twice the work.
B) the same work.
C) four times the work.
D) eight times the work.
5. Potential energy is the energy an object has because of its
A) density.
B) size.
C) position.
D) speed.
E) temperature.
6. The amount of potential energy possessed by an elevated object is equal to
A) the power used to lift it.
B) the distance it is lifted.
C) the force needed to lift it.
D) the work done in lifting it.
E) the value of the acceleration due to gravity.
7. Energy is changed from one form to another with no net loss or gain.
A) Sometimes true
B) Always false
C) Always true
8. As a pendulum swings back and forth
A) at the end points of its swing, its energy is all potential.
B) at the lowest part of its swing, its energy is all kinetic.
C) kinetic energy is transformed into potential energy.
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D)
E)
potential energy is transformed into kinetic energy.
all of the above
9. When a car’s speed triples, its kinetic energy
A) remains the same.
B) triples.
C) increases by four times.
D) increases by nine times.
E) none of the above
10. A job is done slowly, and an identical job is done quickly. Both jobs require the same amount of work but different amounts of
A) energy.
B) power.
C) both A and B
D) none of the above
11. Which requires more work: lifting a 70-kg sack vertically 2 meters or lifting a 35-kg sack vertically 4 meters?
A) Lifting the 70 kg sack
B) Lifting the 35 kg sack
C) Both require the same amount of work.
12. A ball is thrown into the air with 100 J of kinetic energy, which is transformed to gravitational potential energy at the top of its trajectory. When it
returns to its original level after encountering air resistance, its kinetic energy is
A) 100 J.
B) more than 100 J.
C) less than 100 J.
D) Not enough information given.
13. An object that has kinetic energy must be
A) at rest.
B) falling.
C) moving.
D) elevated.
14. Which has greater kinetic energy, a 200 kg SUV traveling at 30 km/h or a 100 kg Prius car traveling at 60 km/h?
A) The 60 km/h car
B) Both have the same kinetic energy.
C) The 30 km/h car
15. Mechanical energy can be in the form of
A) kinetic energy.
B) potential energy.
C) both kinetic and potential energy.
D) neither kinetic nor potential energy.
16. The SI unit of energy is the
A) watt.
B) meter.
C) Newton
D)
E)
second
joule
17. Two balls of equal size are dropped from the same height from the roof of a building. One ball has twice as much mass as the other. How do the
kinetic energies of the two balls compare just before they strike the ground?
A) the lighter one has 1/4th as much KE as the heavier one
B) the lighter one has 1/2 as much KE as the heavier one
C) they both possess the same of KE
D) the lighter one has twice as much KE as the heavier one
E) the lighter on has four times as much KE as the heavier one
18. An arrow in a bow has 70 J of potential energy. Assuming no loss of energy to heat, how much kinetic energy will it have after it has been shot?
A) 0 J
C) 70J
B) 35 J
D) 140J
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C) 50 J
19.
A rock is thrown straight up from the surface of the earth. Which of the following statements describes the energy transformation of the
rock as it rises? Neglect air resistance.
A) the total mechanical energy of the rock increases
B) the kinetic energy of the rock increases and the potential energy decreases
C) both the potential energy and the kinetic energy of the rock increase
D) the kinetic energy decreases and the potential energy increases
E) both the potential energy and the kinetic energy of the rock remain the same
20. The SI unit of power is the
A) newton.
B) meter.
C) joule.
D) second
E) watt
21.
The unit of work is the
A) watt.
B) meter.
C) joule.
D) Newton
E) second
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