Practice: Energy and Work
Level I
1. A fan blows the air and gives it kinetic energy. An hour after the fan has been turned off, what
has happened to the kinetic energy of the air?
(A) it disappears (B) it turns into potential energy (C) it turns into thermal energy (D) it turns
into sound energy (E) it turns into electrical energy
Total energy is always conserved so as the air molecules slow and lose their kinetic energy, there
is a heat flow which increases internal (or thermal) energy
2. A box of old textbooks is on the middle shelf in the bookroom 1.3 m from the floor. If the janitor
relocates the box to a shelf that is 2.6 m from the floor, how much work does he do on the box?
The box has a mass of 10 kg.
(A) 13 J (B) 26 J (C) 52 J (D) 130 J (E) 260 J
3. The figure shows a rough semicircular track whose ends are at a vertical height h. A block placed
at point P at one end of the track is released from rest and slides past the bottom of the track.
Which of the following is true of the height to which the block rises on the other side of the
track?
(A) It is equal to h/(2π) (B) It is equal to h/4
(C) It is equal to h/2 (D) It is equal to h
(E) It is between zero and h; the exact height depends on how much energy is lost to friction.
Since the track is rough there is friction and some mechanical energy will be lost as the block
slides which means it cannot reach the same height on the other side. The extent of energy
lost depends on the surface factors and cannot be determined without more information
4. A 60.0-kg ball of clay is tossed vertically in the air with an initial speed of 4.60 m/s. Ignoring air
resistance, what is the change in its potential energy when it reaches its highest point?
(A) 0 J (B) 45 J (C) 280 J (D) 635 J (E) 2700 J
All of the K = ½ m v2 is converted to U. Simply plug in the values
5. A force F directed at an angle θ above the horizontal is used to pull a crate a distance D across a
level floor. The work done by the force F is
a. FD (B) FD cos θ (C) FD sin θ (D) mg sin θ (E) mgD cos θ
Level II
6. From the top of a 70-meter-high building, a 1-kilogram ball is thrown directly downward with an
initial speed of 10 meters per second. If the ball reaches the ground with a speed of 30 meters
per second, the energy lost to friction is most nearly
(A) 0J (B) 100 J (C) 300 J ( D) 400 J (E) 700 J
Compare the U+K ( mgh + ½ mv2 ) at the top, to the K ( ½ mv2 ) at the bottom and subtract them
to get the loss.
7. A force F at an angle θ above the horizontal 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 frictional force is:
a. –Fd cos θ (B) mgh – Fd cos θ (C) – μ Fd cos θ (D) -μmgd (E) -μ mgd cos θ
8. A ball is thrown upward. At a height of 10 meters above the ground, the ball has a potential
energy of 50 joules (with the potential energy equal to zero at ground level) and is moving
upward with a kinetic energy of 50 joules. Air friction is negligible. The maximum height reached
by the ball is most nearly
(A) 10 m (B) 20 m (C) 30 m (D) 40 m (E) 50 m
First use the given location (h=10m) and the U there (50J) to find the mass.
U=mgh, 50=m(10)(10), so m = 0.5 kg. The total mechanical energy is given in the problem
as U+K = 100 J. The max height is achieved when all of this energy is potential. So set
100J = mgh and solve for h
9. A softball player catches a ball of mass m, which is moving towards her with horizontal speed V.
While bringing the ball to rest, her hand moved back a distance d. Assuming constant
deceleration, the horizontal force exerted on the ball by the hand is
a. mV2/(2d) (B) mV2/d (C) mVd (D) 2mV/d (E) mV/d
10. If the unit for force is F, the unit for velocity V, and the unit for time T, then the unit for energy
is:
(A) FVT (B) F/T (C) FV/T (D) F/T2 (E) FV2/T2
Problem 1
1977 B1. A block of mass 4 kilograms, which has an initial speed of 6 meters per second at time t = 0,
slides on a
horizontal surface.
a. Calculate the work W that must be done on the block to bring it to rest.
If a constant friction force of magnitude 8 Newtons is exerted on the block by the surface, determine the
following:
b. The speed v of the block as a function of the time t.
c. The distance x that the block slides as it comes to rest
1997B1. A 0.20 kg object moves along a straight line. The net force acting on the object varies with the
object's
displacement as shown in the graph above. The object starts from rest at displacement x = 0 and time t = 0
and is
displaced a distance of 20 m. Determine each of the following.
a. The acceleration of the particle when its displacement x is 6 m.
b. The time taken for the object to be displaced the first 12 m.
c. The amount of work done by the net force in displacing the object the first 12 m.
d. The speed of the object at displacement x = 12 m.
e. The final speed of the object at displacement x = 20 m.
Jedi
1979B1. From the top of a cliff 80 meters high, a ball of mass 0.4 kilogram is launched horizontally with
a velocity
of 30 meters per second at time t = 0 as shown above. The potential energy of the ball is zero at the
bottom of the
cliff. Use g = 10 meters per second squared.
a. Calculate the potential, kinetic, and total energies of the ball at time t = 0.
b. On the axes below, sketch and label graphs of the potential, kinetic, and total energies of the ball as
functions of
the distance fallen from the top of the cliff
c. On the axes below sketch and label the kinetic and potential energies of the ball as functions of time
until the ball hits.
Problem 2
2004B1.
A roller coaster ride at an amusement park lifts a car of mass 700 kg to point A at a height of 90 m above
the lowest point on the track, as shown above. The car starts from rest at point A, rolls with negligible
friction down the incline and follows the track around a loop of radius 20 m. Point B, the highest point on
the loop, is at a height of 50 m above the lowest point on the track.
(a)
i. Indicate on the figure the point P at which the maximum speed of the car is attained.
ii. Calculate the value vmsx of this maximum speed.
(b) Calculate the speed vB of the car at point B.
(c)
i. On the figure of the car below, draw and label vectors to represent the forces acting on the car
when it is upside
down at point B.
ii. Calculate the magnitude of all the forces identified in (c)
(d) Now suppose that friction is not negligible. How could the loop be modified to maintain the same
speed at the top of the loop as found in (b)? Justify your answer.