Download PROBLEM SET AP1 Work, Power, Energy, and Energy

AP® Physics 1
Myers Park High School
Problem Set: Work, Power, and Energy
Before completing the problem set read pp. 289 – 315 in your “College Physics” textbook.
A. Work
1. (I) Two students apply a total force of 800 N to push a car 40.0 m across a road. How
much work is done?
2. (I) How much work is done lifting a 60.0 kg crate from the ground to a height of 10.0 m.
3. (I) Using a pulley system, a dockworker does 1920 J of work to lift a crate from one floor
to the next (40.0 m) in a warehouse. What was the tension in the rope?
4. (II) A person pushes a lawnmower with a force of 50.0 N at an angle of 35.0 below the
horizontal. If the mower moves through a distance of 25.0 m, how much work is done by
the person?
5. (II) A person uses a rope to pull a 1000 kg boat 50.0 m along the wharf at constant speed.
The rope makes an angle of 45 with the wharf. The force exerted by the person to move
the boat is 40.0 N. How much work is done on the boat by the water in resisting the
motion of the boat?
6. (III) Calculate the work done in pushing a 4.00 kg block up a frictionless inclined plane
10.0 m long that makes an angle of 30 with the floor. You may assume that the block
moves at constant speed.
7. (III) Calculate the work done lifting the 4.00 kg block in question #6 from the ground to
the top of the inclined plane. (Hint: First find the height of the incline.)
8. (I) How does the work in problem 6 compare to the work in problem 7? Explain.
9. (I)Which force does the most work?
a. The 10 N force
10 N
b. The 8 N force
8N
6N
c. The 6 N force
60o
d. They do the same work
d
d
d
10. (I)A student collects data as a varying force F moves an object to different locations x
along a horizontal plane. If the student plots F vs. x, could it be used to find the work
done on the object while it is moved?
a. Yes, by finding the slope of the best-fit line.
b. Yes, by finding the area between the line and the x axis.
c. Yes, by pick any point on the line and multiply the force coordinate by the
position coordinate.
d. No, it is not possible with this information.
1) 32,000 J
2) 5880 J
3) 48 N
4) 1024 J
5) −1414 J
6) 196 J
7) 196 J
8) same
9) c
10) b
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AP® Physics 1
Myers Park High School
Problem Set: Work, Power, and Energy
B. Power
1. (I) A box that weighs 575 N is lifted a distance of 20.0 m straight up by a rope. The job
is done in 10.0 s. What power is delivered in watts and kilowatts?
2. (I) An electric motor uses 65 kW as it lifts a loaded elevator 17.5 m in 35.0 s. What force
does the motor exert?
3. (I) A boat’s engine pushes it through water at a steady rate of 15 m/s. The force of
friction that acts against the boat is 6000. N. What is the horsepower of the engine?
4. (II) A 300 kg piano is being lifted at a steady speed from ground level straight up to an
apartment 10.0 m above the ground. The crane that is lifting produces a steady power of
400 W. How much time does it take to lift the piano?
5. (II) A 1000 kg car accelerates at 1.25 m/s2 as it goes from 20.0 m/s to 30.0 m/s.
a. What force is applied to the car by its engine (if friction is negligible)?
b. How far does the car travel during this period of acceleration?
c. How much work is done to accelerate the car?
d. How much time elapsed while the car was accelerating?
e. What is the power of the car’s engine?
1) 1150 W; 1.15 kW
2) 1.3 × 105 N
3) 120.6 hp (90 kW)
4) 73.5 s
5) (a) 1250 N (b) 200. m (c) 250. kJ (d) 8.00 s (e) 31.25 kW
C. Energy and Energy Transformations
1. (I)Identify the form of energy and give an example of each.
a. K
b. Ug
c. Us
d. Eth
e. Echem
f. Enuclear
2. (I)Give a specific example of a system with the energy transformation shown where W is
the work done on a system. Any energy not mentioned is assumed to be constant; if work
is not mentioned it is assumed to be zero.
a. W  K
b. W  Ug
c. K  W
d. Ug  K
e. Us  K
f. W  ∆Eth
g. Ug  ∆Eth
h. K  ∆Eth
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AP® Physics 1
Myers Park High School
Problem Set: Work, Power, and Energy
D. Kinetic Energy
1. (I)A rifle can shoot a 4.20 g bullet at a speed of 965 m/s. Find the kinetic energy of the
bullet as it leaves the rifle.
2. (I)A comet with a mass of 7.85 x 1011 kg strikes the earth with a speed of 25.0 km/s.
Find the kinetic energy of the comet in joules.
3. (I)A 1600 kg car has 125 kJ of kinetic energy. What is the speed of the car?
4. (I)An object of mass m is moving with a velocity v has a kinetic energy K. What would
be the kinetic energy of the object if the mass of the object doubles?
5. (I)An object of mass m is moving with a velocity v has a kinetic energy K. What would
be the kinetic energy of the object if the velocity of the object doubles?
6. (II)A stone is dropped from a tower starting from rest. Describe a plot of K vs. t as the
stone falls from release to impact.
7. (I)Rank in order, from greatest to least, the kinetic energies of the sliding pucks.
1 kg
2 m/s
A
1. 1956 J
4. 2K
7. B>D>A=C
1 kg
3 m/s
-2 m/s
1 kg
B
C
2. 2.453 x 1020 J
5. 4K
8.
2 kg
2 m/s
D
3. 12.5 m/s
6. See instructor
9.
E. Gravitational Potential Energy
1. (I) A 50.0 kg shell is shot from a cannon at the Earth’s surface to a height of 425 m.
What is the gravitational potential energy of the shell at this height?
2. (I) How much potential energy does Tim, with a mass of 60.0 kg, gain when he climbs a
gymnasium rope a distance of 3.5 m?
3. (I) Amy raised a 12.0 N physics book from a table 75 cm above the floor to a shelf 2.15
m above the floor. What was the change in potential energy of the book?
4. (II) A 7.26 kg bowling ball hangs from the end of a 2.5 m rope. The ball is pulled back
until the rope makes an angle of 45 with the vertical. What is the increase in the ball’s
potential energy when it is lifted?
5. (II)A stone is dropped from a tower starting from rest. Describe a plot of Ug vs. h as the
stone falls from release to impact.
6. (I)Students are trying to get two packages of equal mass to a balcony of 2nd floor
apartment. Jenny carries her package (A) up a flight of stairs that form on angle of 30o
with the horizontal to get her package to the balcony. Tommy tosses his package (B)
straight up to his buddy Carl on the balcony. Which package has the greatest change in
gravitational potential energy?
1. 208.3 kJ
5. See instructor
2. 2058 J
6. They have the
same change
in Ug.
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3. 16.8 J
7.
4. 52.10 J
8.
AP® Physics 1
Myers Park High School
Problem Set: Work, Power, and Energy
F. Elastic Potential Energy
1. A vertical spring (k = 215 N/m) is compressed a distance of 18 cm. How much potential
energy is stored in the spring?
2. (I) A force of 35 N compresses a spring a distance of 20 cm
a. What is the spring constant for the given spring?
b. How much potential energy is stored in the spring when it is compressed 30
cm?
3. (I) Using a Force vs. Compression/Elongation graph for a given spring, how can the
spring constant be found?
4. (I)A student compresses a spring measuring the elastic potential energy Ug stored in the
spring at certain compression distances x. Using this data, what can be plotted to produce
a linear graph, where the spring constant is the slope or part of the slope?
5. If a spring stretched to a distance x stores a potential energy U. If the spring is
compressed a distance 2x, how much potential energy will be stored?
1. 3.48 J
2.
4. See instructor
(a) 175 N/m (b) 7.875
J
5. 4Us
3. Slope of line
6.
G. Choosing an Isolated System
H. Work, Energy, and Energy Conservation
hA
1. Derive an equation that defines the speed of the mass at B if it is released from rest at point A.
2. A ball of mass m is dropped from a height h onto a vertical spring of constant k. Derive an
equation that defines the distance the spring will be compressed.
3. If a spring stretched to a distance x stores a potential energy U. If the spring is compressed a
distance 2x, how much potential energy will be stored?
4. A spring (spring constant K) is compressed a distance x. The spring is then used to launch a toy
car mass m giving it a velocity v. If the spring is compressed a distance 2x, with what velocity
will the car be launched?
5. A spring (spring constant K) is compressed a distance x. The spring is then used to launch a toy
car mass m giving it a velocity v. If the spring is replaced with a spring of constant 2k, with what
velocity will the car be launched?
6. A ball of mass m is dropped from a height h, derive an equation that defines the velocity of the
ball at impact?
7. A marble of mass m is placed at the L mark on the incline as shown below. The marble is
released from rest.
a. Derive and equation that defines the speed of the marble at the bottom of the incline?
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AP® Physics 1
Myers Park High School
Problem Set: Work, Power, and Energy
b. If the marble continues at that speed along the flat surface, derive and equation that
defines the distance the spring (spring constant k) would be compressed?
L
θ
1) 𝑣 = √2𝑔(ℎ𝐴 − ℎ𝐵 )
2)𝑥 = √
5) √2𝑣
6) 𝑣 = √2𝑔ℎ
3) 4U
2𝑚𝑔ℎ
𝑘
4) 2v
7) a. 𝑣 = √2𝑔𝐿𝑠𝑖𝑛𝜃
2𝑚𝑔𝐿𝑠𝑖𝑛𝜃
𝑘
b. 𝑥 = √
8. If the ball shown in the diagram above is released from rest at point A. Calculate the speed of the
ball at points B and C.
9. An 8.5 kg object is moves at a constant speed of 5.15 m/s for 8.50 s. What it the kinetic energy of
the object during the 8.50 s time interval?
10. A 0.25 kg object rests on a table that has a flat surface 1.45 m off the floor. The object is then
raised 0.500 m above the surface of the table.
a. What is the gravitational potential energy of the object relative to the floor?
b. What is the gravitational potential energy of the object relative to the table?
11. A 450 kg car starts from rest and reaches a speed of 10.5 m/s as it travels along a level surface.
How much work is done on the car as it accelerates?
12. A vertical spring (k = 215 N/m) is compressed a distance of 18 cm.
a. How much potential energy is stored in the spring?
b. The compressed spring is used to launch a 0.35 kg toy rocket into the air. What is the
speed of the rocket when the spring is uncompressed at its equilibrium position? (NOTE:
Ignore the change in gravitational potential energy as the spring returns to its
equilibrium position.)
c. How high above the uncompressed spring will the rocket rise?
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AP® Physics 1
Myers Park High School
Problem Set: Work, Power, and Energy
13. A rifle can shoot a 3.95 g bullet at a speed of 975 m/s.
a. What is the kinetic energy of the bullet as it leaves the riffle?
b. What is the work done on the bullet by the riffle if the bullet started from rest?
c. If the barrel of the rifle is 75 cm in length, what was the average force exerted on the
bullet by the rifle while in the barrel?
14. A 375 g marble is placed at the start of a track at ground level as shown below. The marble
compresses a spring with spring constant 175 N/m a distance of 40.0 cm.
a. How much elastic potential energy is stored in the spring in this initial state?
b. When the marble is released, it rolls in a straight path along the level track. Determine the
speed of the marble a short time after it has been launched by the spring, assuming the
effects of rolling friction on the marble are negligible.
c. If the marble reaches a section of track that slopes upward, what height above ground
level will the marble reach before coming to a stop and rolling back down?
15. A 425 g marble is placed at the 4.00 m mark on the incline as shown below. The marble is
released from rest.
a. What is the speed of the marble at the bottom of the incline?
b. If the marble continues at that speed along the flat surface, how far would it compress a
spring whose spring constant is 200 N/m?
4m
30˚
8) a. 8.85 m/s
b. 6.26 m/s
12) a. 3.48 J b. 4.46
m/s
c. 1.01 m
9) 113 J
10) a. 4.78 J b. 1.22 J
11) 24,800 J
13) a. 1880 J b. 1880 J
c. 2510 N
14. a. 14.0 J b. 8.64
m/s
c. 3.81 m
15) a. 6.26 m/s
b. 0.289 m
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AP® Physics 1
Myers Park High School
Problem Set: Work, Power, and Energy
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