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Take home test due Friday, January 9th
Work and Energy
MPC
1) Person X pushes twice as hard against a stationary brick wall as person Y. Which one of the
following statements is correct?
A) Both do positive work, but person X does four times the work of person Y.
B) Both do positive work, but person X does twice the work of person Y.
C) Both do the same amount of positive work.
D) Both do zero work.
E) Both do positive work, but person X does one-half the work of person Y.
2) A 35-N bucket of water is lifted vertically 3.0 m and then returned to its original position.
How much work did gravity do on the bucket during this process?
A) 180 J
B) 90 J
C) 45 J
D) 0 J
E) 900 J
3) Which one has larger kinetic energy: a 500-kg object moving at 40 m/s or a 1000-kg object
moving at 20 m/s?
A) The 500-kg object
B) The 1000-kg object
C) Both have the same kinetic energy.
4) A stone is held at a height h above the ground. A second stone with four times the mass of the
first one is held at the same height. The gravitational potential energy of the second stone
compared to that of the first stone is
A) one-fourth as much.
B) one-half as much.
C) twice as much.
D) four times as much.
E) the same.
5) You and your friend, who weighs the same as you, want to go to the top of the Eiffel Tower.
Your friend takes the elevator straight up. You decide to walk up the spiral stairway, taking
longer to do so. Compare the gravitational potential energy of you and your friend, after you both
reach the top.
A) It is impossible to tell, since the times you both took are unknown.
B) It is impossible to tell, since the distances you both traveled are unknown.
C) Your friend's gravitational potential energy is greater than yours, because he got to the top
faster.
D) Both of you have the same amount of gravitational potential energy at the top.
E) Your gravitational potential energy is greater than that of your friend, because you traveled a
greater distance in getting to the top.
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6) A heavy dart and a light dart are launched horizontally on a frictionless table by identical ideal
springs. Both springs were initially compressed by the same amount. Which of the following
statements about these darts are correct? (There could be more than one correct choice.)
A) The darts both have the same kinetic energy just as they move free of the spring.
B) The lighter dart leaves the spring moving faster than the heavy dart.
C) The heavy dart had more initial elastic potential energy than the light dart.
D) Both darts move free of the spring with the same speed.
E) Both darts had the same initial elastic potential energy.
7) When you throw a pebble straight up with initial speed V, it reaches a maximum height H with
no air resistance. At what speed should you throw it up vertically so it will go twice as high?
A) 16V
B) 8V
C) 4V
D) 2V
E) V
8) Two frisky otters slide down frictionless hillsides of the same height but different slopes. The
slope of the hill of otter 1 is 30°, while the slope of the hill of otter 2 is 60°. If both start from
rest, which otter is moving faster when she reaches the bottom of her hill?
A) Otter 1 is moving faster.
B) Otter 2 is moving faster.
C) The heavier otter is moving faster, no matter which hill she used.
D) Both otters have the same speed at the bottom.
E) The otter that took the shorter time is moving faster.
9) A stone can slide down one of four different frictionless ramps, as shown in the figure. For
which ramp will the speed of the ball be the greatest at the bottom?
A) Ramp X
B) Ramp Y
C) Ramp Z
D) The speed of the ball will be the same for all ramps.
10) Two identical grasshoppers jump into the air with the same initial speed and experience no
air resistance. Grasshopper A goes straight up, but grasshopper B goes up at a 66° angle above
the horizontal. Which of the following statements about these grasshoppers are correct? (There
could be more than one correct choice.)
A) At their highest point, both of them have the same amount of gravitational potential energy.
B) At their highest point, both of them have the same amount of kinetic energy.
C) At their highest point, both of them have the same amount of mechanical energy.
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D) At their highest point, grasshopper B is moving faster than grasshopper A.
E) At their highest point, grasshopper A has more gravitational potential energy than grasshopper
B.
11) A force produces power P by doing work W in a time T. What power will be produced by a
force that does six times as much work in half as much time?
A) 12P
B) 6P
C) P
D) P
E)
P
12) How much work would a child do while pulling a 12-kg wagon a distance of
force?
A) 95 J
B) 52 J
C) 67 J
D) 109 J
with a
13) A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If
of work are
done by the strap while moving the suitcase a horizontal distance of
what is the tension in
the strap?
A) 46 N
B) 37 N
C) 52 N
D) 56 N
14) A person carries a 2.00-N pebble through the path shown in the figure, starting at point A
and ending at point B. The total time from A to B is 6.75 min. How much work did gravity do on
the rock between A and B?
A) 30.0 J
B) -30.0 J
C) -56.0 J
D) 56.0 J
E) -36.0 J
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15) How much kinetic energy does a 0.30-kg stone have if it is thrown at
A) 290 J
B) 580 J
C) 440 J
D) 510 J
16) When a car of mass
accelerates from 10.0 m/s to some final speed, 4.00 × 105 J of
work are done. Find this final speed.
A) 28.0 m/s
B) 22.4 m/s
C) 25.2 m/s
D) 30.8 m/s
17) How large a net force is required to accelerate a 1600-kg SUV from rest to a speed of 25 m/s
in a distance of 200 m?
A) 1600 N
B) 0 N
C) 200 N
D) 400 N
E) 2500 N
18) A 100-N force has a horizontal component of 80 N and a vertical component of 60 N. The
force is applied to a cart on a level frictionless floor. The cart starts from rest and moves 2.0 m
horizontally along the floor due to this force. What is the cart's final kinetic energy?
A) 200 J
B) 160 J
C) 120 J
D) zero
19) A 1000-kg car experiences a net force of 9500 N while slowing down from 30 m/s to
How far does it travel while slowing down?
A) 34 m
B) 31 m
C) 37 m
D) 41 m
20) A stone initially moving at 8.0 m/s on a level surface comes to rest due to friction after it
travels 11 m. What is the coefficient of kinetic friction between the stone and the surface?
A) 0.13
B) 0.25
C) 0.30
D) 0.43
E) 0.80
21) A sled having a certain initial speed on a horizontal surface comes to rest after traveling 10
m. If the coefficient of kinetic friction between the object and the surface is 0.20, what was the
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initial speed of the object?
A) 9.8 m/s
B) 6.3 m/s
C) 3.6 m/s
D) 7.2 m/s
E) 8.9 m/s
22) It takes 87 J of work to stretch an ideal spring from 1.4 m to 2.9 m from equilibrium. What is
the value of the spring constant (force constant) of this spring?
A) 27 N/m
B) 77 N/m
C) 52 N/m
D) 39 N/m
23) A rock falls from a vertical cliff that is 4.0 m tall and experiences no significant air resistance
as it falls. At what speed will its gravitational potential energy (relative to the base of the cliff) be
equal to its kinetic energy?
A) 3.1 m/s
B) 4.4 m/s
C) 6.3 m/s
D) 8.9 m/s
E) 13 m/s
24) A block slides down a frictionless inclined ramp and experiences no significant air
resistance. If the ramp angle is 17.0° above the horizontal and the length of the surface of the
ramp is
find the speed of the block as it reaches the bottom of the ramp, assuming it
started sliding from rest at the top.
A) 10.7 m/s
B) 114 m/s
C) 7.57 m/s
D) 19.6 m/s
25) A bead is moving with a speed of 20 m/s at position A on the track shown in the figure. This
track is friction-free, and there is no appreciable air resistance. What is the speed of the bead at
point C?
A) 0 m/s
B) 34 m/s
C) 69 m/s
D) 20 m/s
E) We cannot solve this problem without knowing the mass of the bead.
26) The figure shows a famous roller coaster ride. You can ignore friction. If the roller coaster
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leaves point Q from rest, what is its speed at the top of the 25-m peak (point S)?
A) 10 m/s
B) 22 m/s
C) 44 m/s
D) 62 m/s
E) 120 m/s
27) A toy rocket that weighs 10 N blasts straight up from ground level with an initial kinetic
energy of 40 J. At the exact top of its trajectory, its total mechanical energy is 140 J. To what
vertical height above the ground does it rise, assuming no air resistance?
A) 1.0 m
B) 10 m
C) 14 m
D) 24 m
28) A roller coaster starts from rest at a height h at the left side of a loop-the-loop, as shown in
the figure. It is not attached to the track in anyway, and there is no friction from the track or from
air resistance. If the radius of the loop is R = 6.0 m, what is the minimum height h for which the
roller coaster will not fall off the track at the top of the loop?
A) 21 m
B) 18 m
C) 15 m
D) 12 m
E) 8.5 m
29) A child pulls on a wagon with a force of
If the wagon moves a total of
what is the average power delivered by the child?
A) 17 W
B) 21 W
C) 22 W
D) 26 W
30) If electricity costs 7.06¢/kW·h, how much would it cost you to run a
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in
stereo system
per day for
A) $0.95
B) $0.14
C) $1.62
D) $2.66
Free response
1) A 500-kg elevator is pulled upward with a constant force of 5500 N for a distance of 50.0 m.
(a) What is the work done by the 5500-N force?
(b) What is the work done by gravity?
(c) What is the net work done on the elevator?
2) A 2.0-kg object is lifted vertically through 3.00 m by a 150-N force. How much work is done
on the object by gravity during this process?
3) How fast must a 6.0-kg cat run to have a kinetic energy of 150 J?
4) How high a hill would a 75-kg hiker have to climb to increase her gravitational potential
energy by 10,000 J?
5) You want to store 1,000 J of energy in an ideal spring when it is compressed by only 2.5 cm.
What should be the force constant (spring constant) of this spring?
6) A frictionless simple pendulum, with a small but dense 4.4-kg mass at the end and a length of
75 cm, is released from rest at an angle of 50° with the vertical.
(a) To what height above its lowest point does the mass swing on the other side?
(b) What is the speed of the mass at the bottom of the swing?
7) A roller coaster starting from rest descends 35 meters in its initial drop and then rises 23
meters when it goes over the first hill, which has a circular shape over the top. If a passenger at
the top of the hill feels an apparent weight equal to one-half of her normal weight, what is the
radius of curvature of the first hill? Neglect any frictional losses.
8) A 7.5-kg otter slides down a hill, starting from rest at the top. The sloping surface of the hill is
8.8 m long, and the top is 6.5 m above the base. If the speed of the otter at the bottom of the hill
is 9.2 m/s, how much energy was lost to non-conservative forces on the hill?
9) Rita raises a 10kg package to a height of 2.5 m in 2.0 s.
(a) How much work did she do on the package?
(b) How much power was expended on the package?
(c) If she were to raise the package in 1.0 s rather than 2.0 s, how do the work and power
change?
10) In a physical fitness program, a woman who weighs 510 N runs up four flights of stairs in 22
s. Each flight rises 3.1 m. (1 hp = 746 W)
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(a) What is her total change in potential energy?
(b) What was the minimum average power (in watts) that she expended during the 22 s?
(c) What horsepower motor would be required to generate the same power?
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