Work & Power
AP Physics
Work, Power & Energy
Name:
Problem Set
A> Work: Assume motion is constant unless otherwise stated.
1) Two students apply a total force of 800. N
7) Calculate the work done in pushing a 4.00 kg
to push a car 40.0 m across a road. How
block up a frictionless inclined plane 10.0 m
much work is done?
long that makes an angle of 30 with the
floor. You may assume that the block moves
2) How much work is done lifting a 60.0 kg
at constant speed.
crate from the ground to a height of 10.0 m.
8) Calculate the work done lifting the 4.00 kg
3) Using a pulley system, a dockworker does
block in question #7 from the ground to the
1920 J of work to lift a crate from one floor
top of the inclined plane. (Hint: First find
to the next (40.0 m) in a warehouse. What
the height of the incline.)
was the tension in the rope?
9) How does the work in problem 7 compare to
4) A person pushes a lawnmower with a force of
the work in problem 8. Explain.
50.0 N at an angle of 35.0 below the
horizontal. If the mower moves through a
10) It takes 12.0 kJ of work to pull a loaded sled
distance of 25.0 m, how much work is done
weighing 800 N a distance of 200. m. To do
by the person?
this, a force of 120 N is exerted on the rope
that makes an angle with the horizontal. At
5) In order to change a tire, a force of 80.0 N
what angle is the rope held?
is exerted on the handle of a screw type
jack. The handle to which the steel shaft is
11) The hammer of a pile driver has a mass of
attached has a radius of 0.50 m. The handle
100.0 kg. The machine’s engine lifts it to a
is turned through 30 revolutions. How much
height of 5.0 m every 10.0 s.
work is done?
a) How much work does the machine do to
lift the hammer?
6) A person uses a rope to pull a 1000. kg boat
b) How much work does the machine do in one
50.0 m along the wharf at constant speed.
minute?
The rope makes an angle of 45 with the
c) How much work is done by gravity as the
wharf. If a force of 40.0 N is used to move
machine lifts the hammer?
the boat, how much work is done on the boat
d) How much work is done by gravity as the
by the water?
hammer is dropped?
1) 32 kJ
2) 5880 J
3) 48 N
6) -1414 J
7) 196 J
8) 196 J
12) (a) 4900 J (b) 2.94 x 104 J (c) –4900 J (d) 4900 J
B> Power:
1) 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)
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?
4) 1020 J
10) 60
3)
5) 7540 J
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 power of the engine?
4)
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)
A 1000. kg car accelerates at 1.25 m/s2 as it
goes from 20.0 m/s to 30.0 m/s.
1) 1150 W; 1.15 kW
2) 1.3 x 105 N
5) (a) 1250 N (b) 200. m (c) 250. kJ (d) 8.00 s (e) 31.3 kW
(a) What force is applied to the car by its
engine?
(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?
3) 90 kW
4) 73.5 s
C> Kinetic Energy:
1)
How much work is done to slow an 875 kg
compact car from 44.0 m/s to 22.0 m/s?
2)
3)
7)
A racing car has a mass of 1525 kg. What is
its kinetic energy of it has a speed of 108
km/h?
If the car from problem # 1 was moving at
44.0 m/s, how much work would be done to
stop the car?
8)
A rifle can shoot a 4.20 g bullet at a speed
of 965 m/s.
(a) Find the kinetic energy of the bullet as
it leaves the rifle.
(b) What work is done on the bullet if it
starts from rest?
(c) If the work is done over a distance of
75 cm, what is the average force on the
bullet?
(d) If the bullet comes to rest by
penetrating 1.5 cm into metal, what is
the magnitude and direction of the
force the metal exerts on the bullet?
Toni has a mass of 45 kg and is moving with a
speed of 10.0 m/s
(a) What is Toni’s kinetic energy?
(b) Toni’s speed is reduced to half as much
(5.0 m/s). What is her kinetic energy
now?
(c) What is the ratio of the kinetic energies
in parts a and b? Why isn’t it 2 to 1?
9)
Shawn and his bike have a total mass of 45.0
kg. Shawn rides his bike 1.80 km in 10.0
minutes at a constant velocity. What is
Shawn’s kinetic energy?
4)
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.
10) In the 1950’s, an experimental train that had
a mass of 2.5 x 104 kg was powered across a
level track by a jet engine that produced a
thrust of 5.00 x 105 N for a distance of 509
m. Find the final speed of the train if it
started from rest and friction was negligible.
5)
Accelerating a 5700 kg trailer truck from
rest to 100 km/h requires 2.2 x 106 J.
(a) What would be the truck’s speed if half
as much work were done on it?
(b) What would be the truck’s speed if
twice as much work were done on it?
11) A 14,700 N car is traveling at 25 m/s. The
brakes are applied suddenly, and the car
slides to a stop. The average braking force
between the tires and the road is 7100 N.
How far will the car slide once the brakes
are applied?
6)
A 1600 kg car travels at a speed of 12.5 m/s.
What is its kinetic energy?
1)
4)
8)
-6.35 x 105 J
2) -8.47 x 105 J
3) (a) 1960 J (b) 1960 J (c) 2600 N (d) 1.3 x 105 N backward
20
2.45 x 10 J
5) (a) 71 km/h (b) 140 km/h
6) 1.3 x 105 J
7) 686 kJ
(a) 2300 J (b) 560 J (c) 4 to 1
9) 203 J
10) 143 m/s
11) 66 m
D> Potential Energy:
1)
2)
3)
A 90 kg rock climber 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 at the top and at the
bottom.
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?
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?
4)
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?
1)
5)
top: 4 x 104J; bottom: -4 x 104 J
130 J
6) –2780 J
2)
7)
5)
A 6.5 kg bowling ball is lifted 2.1 m into a
storage rack. Calculate the increase in the
ball’s potential energy.
6)
Mary weighs 505 N. She walks down a flight
of stairs to a level 5.50 m below her starting
position. What is the change in Mary’s
potential energy?
7)
A weightlifter raises a 180 kg barbell to a
height of 1.95 m. How much work is done on
the barbell?
8)
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?
9)
If 1.00 J of work is done to lift a block 1.00
m, what is the mass of the block?
2.08 x 105 J
3400 J
3)
8)
52 J
16.8 J
4)
9)
2.1 kJ
0.10 kg
E> Conservation of Energy:
1)
2)
A 15.0 kg model airplane flies horizontally at
12.5 m/s.
a) Determine the kinetic energy of the
plane.
b) The plane goes into a dive and levels off
20.4 m closer to the ground. How much
potential energy did the plane lose during
the dive?
c) What was the change in kinetic energy of
the plane during the dive?
d) What is the plane kinetic energy at this
lower altitude?
e) What is the plane’s speed at this lower
altitude?
A partially filled bag of cement having a mass
of 16.0 kg falls 40.0 m from a bridge.
a) What was the kinetic energy of the bag
just as it strikes the ground?
b) With what speed will the bag of cement
impact the ground?
3)
A 98.0 N block falls 64.0 m.
a) What is the potential energy of the block
before it begins to fall?
b) What is the kinetic energy of the block
just as it strikes the ground?
c) What is the speed of the block upon
impact?
4)
During a hammer throw at a track meet, an
8.0 kg hammer is accidentally thrown
straight up into the air. If the release speed
of the hammer is 14.0 m/s, how high will the
hammer rise above its release position?
5)
A 98.0 N test rocket is fired from Kennedy
Space Center. Its fuel provides 1960 J
before it leaves the launch pad. How high
will the rocket rise?
6)
7)
In an electronics factory, small cabinets
slide down a 30 incline for a distance of 16.0
m to reach the next assembly stage. The
cabinets each have a mass of 10.0 kg.
a) What is the speed of the cabinets as
they reach the bottom of the incline?
b) How much kinetic energy do the cabinets
have at this point?
8)
A motorcyclist is trying to leap across a
canyon by driving horizontally off the cliff at
a speed of 38.0 m/s. Find the speed with
which the cyclist strikes the ground on the
other side.
A biker approaches a hill with a speed of 8.5
m/s.
a) Write an expression for representing the
kinetic energy of the biker at the bottom
of the hill.
b) Write an expression for the potential
energy of the biker at the top of the hill.
c) Using these two expressions, how high up
the hill will the biker be when he stops?
1) (a) 1170 J (b) 3000 J (c) 3000 J (d) 4170 J (e) 23.6 m/s
3) (a) 6270 J (b) 6270 J (c) 35.4 m/s
4) 10. m
6) (a) 12.5 m/s (b) 784 J
7) 3.69 m
2) (a) 6270 J (b) 28.0 m/s
5) 20. m
8) 46.2 m/s