Physics: Energy Work and Power Practice Guide
Massachusetts State Standards:
2. Conservation of Energy and Momentum
Central Concept: The laws of conservation of energy and momentum provide
alternate approaches to predict and describe the movements of objects.
2.1 Interpret and provide examples that illustrate the law of conservation of
energy.
2.2 Interpret and provide examples of how energy can be converted from
gravitational potential energy to kinetic energy and vice versa.
2.3 Describe both qualitatively and quantitatively how work can be expressed as a
change in mechanical energy.
2.4 Describe both qualitatively and quantitatively the concept of power as work
done per unit time.
Essential Questions:
1.
2.
How do we know when an object has energy?
How does understanding the Law of Conservation of Energy allow us to explain the world around us?
Guiding Questions:
3.
4.
How do you define work in terms of force and displacement?
How do you find the work done by a constant force when the force and displacement vectors are at an
angle?
5. How can work be determined from a force versus displacement graph?
6. What are the types of mechanical energy?
7. What is the difference between kinetic and potential energy?
8. What is the work energy theorem?
9. How do conservative and non-conservative forces differ?
10. What is the law of conservation of energy?
11. How is the law of conservation of energy applied?
12. What is power in the scientific sense?
1
I have no idea
I kind of know what this is, but
could not test well
I have a moderate grasp
of this concept
I know what this is and could test
well
I have a thorough understanding
and could teach this to another
1.
2.
3.
4.
5.
PHYSICS CHART OF UNDERSTANDING
MECHANICAL ENERGY UNIT:
(RATE YOUR UNDERSTANDING OF THE OBJECTIVES)
1. Define and quantify work
2. Identify forms of mechanical energy and types that are not mechanical
3. Define and quantify kinetic energy
4. Define and quantify gravitational potential energy
5. Describe how energy can be transferred from one form into another
6. Calculate work done from a Force vs. time graph
7. Describe the law of conservation of energy
8. Distinguish between conservative and non-conservative forces
9. Apply the law of conservation of energy to determine initial and final
values for energy and work
10. Describe the relationship between spring displacement and force
11. Define and quantify a relationship between spring displacement and
elastic potential energy
12. Define and Calculate power
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QUICK REFERENCE
Important Terms
conservative force
a force which does work on an object which is independent of the path taken by the
object between its starting point and its ending point
conserved properties
any properties which remain constant during a process
energy
the non-material quantity which is the ability to do work on a system
joule
the unit for energy equal to one Newton-meter
kinetic energy
the energy a mass has by virtue of its motion
law of conservation of energy
the total energy of a system remains constant during a process
mechanical energy
the sum of the potential and kinetic energies in a system
non-conservative work
work that is done
potential energy
the energy an object has because of its position
power
the rate at which work is done or energy is dissipated
watt
the SI unit for power equal to one joule of energy per second
work
the scalar product of force and displacement
*Level Differentiation Key: All levels are to do conceptual problems and
application problems denoted with an (I). Honors level courses are to do all
problems, including those denoted with (II)
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Define and Quantify Work
Key Concept(s):
Conceptual Example 1: Which is more work: rolling a wagon 2m forward OR lifting a wagon 2m
upwards? Why?
Conceptual Example 2: Compare the amount of energy exerted by a weight lifter who bench presses
500N ten times to another lifter whom “maxes out” at 1000N for one repetition.
Conceptual Example 3:
If the work done by a force on an object is not zero then the force is said to be
a. Conservative
b. Non-conservative
c. zero
d. left wing
e. none of the above
Conceptual Example 4:
Which of the following are true concepts about work?
a. work describes the position of an object as a function of time.
b. the work done on an object is always independent of the path.
c. the work done on an object depends on its path.
d. work is a force
e. work provides a link between force and energy.
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Application Example 1: A 1300-N crate rests on the floor. How much work is required to move it at
constant speed (a) 4.0 m along the floor against a friction force of 230 N, and (b) 4.0 m vertically?
Application Example 2: (I) How much work did the movers do (horizontally) pushing a 160-kg crate
10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0.50?
Application Example 3: (II) A box of mass 5.0 kg is accelerated by a force across a floor at a rate of
2.0 m s 2 for 7.0 s. Find the net work done on the box.
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Work, Varying Force (Graphs)
Key Concept(s):
Example 1:
The force on an object, acting along the x axis, varies as shown in Fig. 6–37. Determine the work done by
this force to move the object (a) from x 0.0 to x 10.0 m, and (b) from x 0.0 to x 15.0 m.
Example 2:
In Fig. 6–6a, assume the distance axis is linear and that d A 10.0 m and d B 35.0 m.
Estimate the work done by force F in moving a 2.80-kg object from d A to d B .
Example 3:
An object with a mass of 2 kg is initially at rest at a position x = 0. A nonconstant force F is applied to the object over 6 meters.
What is the total work done on the object at the end of 6 meters?
(A) 200 J
(B) 150 J
(C) 170 J
(D) 190 J
(E)180 J
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Kinetic Energy
Key Concept(s):
Conceptual Example 1:
A car moves with speed of 20 m/s then speeds up to achieve a speed of 40 m/s at the bottom, how
many times greater is the new kinetic energy of the car?
a.
b.
c.
d.
e.
Half as much
The same
√2 times as great
Twice as great
Four times as great
Conceptual Example 2:
A 80kg bicyclist applies a 200N force to increase his bicycles speed over 10m. Assuming no energy is lost
to other forms, the amount of Kinetic Energy gained by the bike is:
a.
b.
c.
d.
Equal to the work done by the bicyclist pedaling
Half the work done by the cyclist
Double the work done by the cyclist
Exactly 160000J
Conceptual Example 3:
Car #1 has twice the mass of car #2, but they both have the same kinetic energy. How do their
speeds compare?
a)
b)
c)
d)
e)
2 v1 = v2
2 v1 = v2
4 v1 = v2
v1 = v2
8 v1 = v2
Application Example 1: (I) How much work must be done to stop a 1250-kg car traveling at 105 km h ?
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Application Example 2: (II) An 88-g arrow is fired from a bow whose string exerts an average force of
110 N on the arrow over a distance of 78 cm. What is the speed of the arrow as it leaves the bow?
Application Example 3:(II) A baseball m 140 g traveling 32 m s moves a fielder’s glove backward 25
cm when the ball is caught. What was the average force exerted by the ball on the glove?
ADDITIONAL EXAMPLE: If it takes 4,000J of to accelerate an object from
0m/s to 10m/s over 10m
a) How much energy is required to change it from 10m/s to 20m/s?
b) Assuming the same force is applied as previously, how much
distance would be covered between 10m/s and 20m/s?
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Gravitational Potential Energy
Key Concept(s):
Example 1: (I) A 7.0-kg monkey swings from one branch to another 1.2 m higher. What is the change in
potential energy?
Example 2: (I) By how much does the gravitational potential energy of a 64-kg pole vaulter change if his
center of mass rises about 4.0 m during the jump?
Example 3: (II) A 55-kg hiker starts at an elevation of 1600 m and climbs to the top of a 3300-m peak. (a)
What is the hiker’s change in potential energy? (b) What is the minimum work required of the
hiker?
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Elastic Potential Energy
Key Concept(s):
Example 1: (I) A spring has a spring stiffness constant, k, of 440 N m . How much must this spring be
stretched to store 25 J of potential energy?
Example 2: (II) A 1200-kg car rolling on a horizontal surface has speed v 65 km h when it strikes a
horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness
constant of the spring?
Example 3: (II) A spring with k 53 N m hangs vertically next to a ruler. The end of the spring is next to
the 15-cm mark on the ruler. If a 2.5-kg mass is now attached to the end of the spring, where will
the end of the spring line up with the ruler marks?
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Conservation of Mechanical Energy
Key Concept(s):
Conceptual Example 1:
A 80kg bicyclist applies a 200N force to increase his bicycles speed over 10m. Assuming no energy is lost
to other forms, the amount of Kinetic Energy gained by the bike is:
a.
b.
c.
d.
Equal to the work done by the bicyclist pedaling
Half the work done by the cyclist
Double the work done by the cyclist
Exactly 160000J
Conceptual Example 2:
A child slides down a hill that is 5m tall. Assuming no non-conservative forces (such as friction) are
present, the speed of the child at the bottom of the hill is:
a.
b.
c.
d.
e.
5m/s
10m/s
15m/s
20m/s
Not given
Conceptual Example 3:
Introduce friction for the child on the sled case described above, if the child had 2000J of potential
energy at the top, but they only have 1200J of kinetic energy at the bottom of the hill, how much
energy was converted into heat?
a.
b.
c.
d.
e.
800J
3200J
1.6J
0.6J
Not given
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Application Example 1. (I) Jane, looking for Tarzan, is running at top speed 5.3 m s and grabs a vine
hanging vertically from a tall tree in the jungle. How high can she swing upward? Does the length
of the vine affect your answer?
Example 2:
(I*II**) In the high jump, Fran’s kinetic energy is transformed into gravitational potential energy without
the aid of a pole. With what minimum speed must Fran leave the ground in order to lift her center of
mass 2.10 m* and cross the bar with a speed of 0.70 m s ? **
Example 3:
(II) A 65-kg trampoline artist jumps vertically upward from the top of a platform with a speed of 5.0 m s .
(a) How fast is he going as he lands on the trampoline, 3.0 m below (Fig. 6–38)? (b) If the trampoline
behaves like a spring with spring stiffness constant 6.2 10 4 N m , how far does he depress it?
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Sample Energy Multi-Choice Problems:
1. A driver in a 2000 kg Porsche wishes to pass a slow moving school bus on a 4 lane road. What is the
average power in watts required to accelerate the sports car from 30 m/s to 60 m/s in 9 seconds?
(A) 1,800
(B) 5,000
(C)10,000
(D)100,000
(E) 300,000
2. A force F is at an angle θ above the horizontal and is used to pull a heavy suitcase of weight mg a
distance d along a level floor at constant velocity. The coefficient of friction between the floor and the
suitcase is μ. The work done by the force F is:
(A)Fdcos θ - μmgd
(B) Fdcos θ
(C) -μmgd
(D) 2Fdsin θ - μmgd
(E) Fdcos θ – 1
3. A force of 20 N compresses a spring with a spring constant 50 N/m. How much energy is stored in the
spring?
(A) 2 J
(B) 5 J
(C) 4 J (D) 6 J
(E) 8 J
4. A stone is dropped from the edge of a cliff. Which of the following graphs best represents the
stone's kinetic energy KE as a function of time t?
(A)
(B)
(D)
(C)
(E)
5. A 4 kg ball is attached to a 1.5 m long string and whirled in a horizontal circle at a constant speed 5
m/s. How much work is done on the ball during one period?
(A) 9 J
(B) 4.5 J
(C) zero
(D) 2 J
(E) 8 J
6. A student pushes a box across a horizontal surface at a constant speed of 0.6 m/s. The box has a
mass of 40 kg, and the coefficient of kinetic friction is 0.5. The power supplied to the box by the
person is
(A) 40 W
(B) 60 W
(C) 150 W
(D) 120 W
(E) 200 W
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7. A force F is applied in horizontal to a 10 kg block. The block moves at a constant speed 2 m/s across
a horizontal surface. The coefficient of kinetic friction between the block and the surface is 0.5. The
work done by the force F in 1.5 minutes is:
(A) 9000 J (B) 5000 J (C) 3000 J (D) 2000 J (E) 1000 J
Questions 8-9A ball swings from point 1 to point 3. Assuming
the ball is in SHM and point 3 is 2 m above the lowest point 2.
Answer the following questions.
8. What happens to the kinetic energy of the ball when it moves from point 1 to point 2?
(A) increases (B) decreases (C) remains the same (D) zero (E) more information is required
9. What is the velocity of the ball at the lowest point 2?
(A) 2.2 m/s (B) 3.5 m/s (C) 4.7 m/s (D) 5.1 m/s (E) 6.3 m/s
10. A block with a mass of m slides at a constant velocity V0 on a horizontal frictionless surface. The
block collides with a spring and comes to rest when the spring is compressed to the maximum value.
If the spring constant is K, what is the maximum compression in the spring?
(A) V0 (m/K)1/2 (B) KmV0(C) V0K/m
(C) m V0/K
(D) V0 (K/m)1/2
(E) (V0m/K)1/2
Questions 11-12
A 2 kg block released from rest from the top of an incline
plane. There is no friction between the block and the
surface.
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11. How much work is done by the gravitational force on the block?
(A) 80 J (B) 60 J
(C) 50 J
(D) 40 J
(E) 30 J
12. What is the speed of the block when it reaches the horizontal surface?
(A) 3.2 m/s
(B) 4.3 m/s
(C) 5.8 m/s
(D) 7.7 m/s
(E) 6.6 m/s
13. A crane lifts a 300 kg load at a constant speed to the top of a building 60 m high in 15 s. The
average power expended by the crane to overcome gravity is:
(A) 10,000 W
(B) 12,000 W
(C) 15,000 W
(D) 30,000 W
(E) 60,000 W
14. A satellite with a mass m revolves around Earth in a circular orbit with a constant radius R. What is
the kinetic energy of the satellite if Earth’s mass is M?
(A) ½ mv2
2Mm/R
(B) mgh
(C) ½GMm/R2
(D) ½ GMm/R (E)
Questions 15-16
An apple of mass m is thrown in horizontal from the edge of a cliff
with a height of H.
15. What is the total mechanical energy of the apple with respect to the ground when it is at the edge
of the cliff?
(A) 1/2mv02
(B) mgH
(C) ½ mv02- mgH
(D) mgH - ½ mv02(E) mgH + ½ mv02
16. What is the kinetic energy of the apple just before it hits the ground?
(A) ½ mv02 + mgH
(B) ½ mv02 - mgH
(C) mgH
(D) ½ mv02 (E) mgh -1/2 mv02
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Questions 17-18A 500 kg roller coaster car starts from rest
at point A and moves down the curved track. Ignore any
energy loss due to friction.
17. Find the speed of the car at the lowest point B.
(A) 10 m/s
(B) 20 m/s
(C) 30 m/s
(D) 40 m/s
(E) 50 m/s
18. Find the speed of the car when it reaches point C.
(A) 10 m/s
(B) 20 m/s
(C) 30 m/s
(D) 40 m/s
(E) 50 m/s
23. A toy car travels with speed V0 at point X. Point Y is a
height H below point X. Assuming there is no frictional
losses and no work is done by a motor, what is the speed at
point Y?
(A)(2gH+1/2 V02)1/2
2gH+ (1/2 V02)1/2
(B) V0-2gH (C) (2gH + V02)1/2
(E) V0+2gH
(D)
24. A rocket is launched from the surface of a planet with
mass M and radius R. What is the minimum velocity the rocket must be given to completely escape from
the planet’s gravitational field?
(A) (2GM/R)1/2 (B) (2GM/R)3
(C) (GM/R)1/2
(D) 2GM/R
(E) 2GM/16R2
25. A block of mass m is placed on the frictionless inclined plane
with an incline angle θ. The block is just in a contact with a free end
on an unstretched spring with a spring constant k. If the block is
released from rest, what is the maximum compression in the
spring?
(A) kmgsinθ
(B) kmgcosθ
(C) 2mg sinθ /k
(E) kmg
(D) mg/k
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Work and Energy Practice Problems
1. E
2. B
3. C
4. B
5. C
6. D
7. A
8. A
9. E
10. A
11. B
12. D
13. B
14. D
15. E
16. A
17. C
18. B
19. B
20. B
21. D
22. B
23. C
24. A
25. C
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