physics chapter 6: work and energy
10) A 4.0 kg object is moving with speed 2.0 m/s. A 1.0 kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force, and are brought to rest. Which object travels the greater distance before stopping? A) the 4.0 kg object B) the 1.0 kg object C) Both objects travel the same distance. D) It cannot be determined from the information given.
C
52) On a horizontal frictionless air table, a puck runs into an ideal horizontal spring that is fastened to the table. The puck compresses the spring by 15 cm before coming to rest. During the compression process, which quantities are conserved? A) only the momentum of the puck B) only the kinetic energy of the puck C) only the mechanical energy (kinetic plus potential) of the puck D) the momentum and the mechanical energy of the puck E) the momentum and the kinetic energy of the puck
C
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.
D
13) 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.
D
22) 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.
D
17) 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
E
23) A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill with no air resistance. Which object rises to a greater height? A) The heavy object, because it has greater initial kinetic energy. B) The light object, because gravity slows it down less. C) The lightweight object, because the force of gravity on it is less. D) The heavy object, because it has more mass to carry it up the hill. E) They both slide to exactly the same height.
E
31) A heavy stone and a light stone are released from rest in such away that they both have the same amount of gravitational potential energy just as they are released. Air resistance is negligibly small. Which of the following statements about these stones are correct? (There could be more than one correct choice.) A) The initial height of the light stone is greater than the initial height of the heavy stone. B) The stones must have been released from the same height. C) The stones both have the same speed just as they reach the ground. D) Just as it reaches the ground, the light stone is traveling faster than the heavy stone. E) The stones both have the same kinetic energy just as they reach the ground.
A,D,E
11) You slam on the brakes of your car in a panic, and skid a certain distance on a straight level road. If you had been traveling twice as fast, what distance would the car have skidded, under the same conditions? A) It would have skidded 4 times farther. B) It would have skidded twice as far. C) It would have skidded 1.4 times farther. D) It would have skidded one half as far. E) It is impossible to tell from the information given.
A
25) Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed twice as high as Bill. If there is no air resistance, the maximum height of Joe's ball will be A) four times that of Bill's ball. B) two times that of Bill's ball. C) equal to that of Bill's ball. D) eight times that of Bill's ball. E) roughly 1.4 times that of Bill's ball.
A
38) Two cyclists who weigh the same and have identical bicycles ride up the same mountain, both starting at the same time. Joe rides straight up the mountain, and Bob rides up the longer road that has a lower grade. Joe gets to the top before Bob. Ignoring friction and wind resistance, which one of the following statements is true? A) The amount of work done by Joe is equal to the amount of work done by Bob, but the average power exerted by Joe is greater than that of Bob. B) The amount of work done by Joe is greater than the amount of work done by Bob, and the average power exerted by Joe is greater than that of Bob. C) Bob and Joe exerted the same amount of work, and the average power of each cyclist was also the same. D) The average power exerted by Bob and Joe was the same, but Joe exerted more work in getting there.
A
40) 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
A
42) In an inelastic collision involving an isolated system, the final total momentum is A) exactly the same as the initial momentum. B) more than the initial momentum. C) less than the initial momentum.
A
45) In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after, are shown. The collision is (PICTURE) A) perfectly elastic B) partially inelastic. C) completely inelastic. D) characterized by an increase in kinetic energy. E) not possible because momentum is not conserved.
A
51) A rubber ball bounces off of a wall with an initial speed v and reverses its direction so its speed is v right after the bounce. As a result of this bounce, which of the following quantities of the ball are conserved? (There could be more than one correct choice.) A) the kinetic energy of the ball B) the momentum of the ball C) both the momentum and the kinetic energy of the ball D) None of the above quantities are conserved.
A
53) Two objects of different mass have equal, non-zero kinetic energies. Which object has the greater magnitude momentum? A) the heavier object B) the lighter object C) They both have the same magnitude momentum.
A
55) If you want to double the kinetic energy of a gas molecule, by what factor must you increase its momentum? A) B) 2 C) 2 D) 4 E) 16
A
57) A firecracker explodes in midair and breaks up into many fragments. Which of the following statements are true regarding conditions immediately before and immediately after the explosion: I. The total momentum of the fragments is equal to the original momentum of the firecracker. II. The total kinetic energy of the fragments is equal to the original kinetic energy of the firecracker. A) Statement I only B) Statement II only C) Both Statement I and Statement II D) Neither statement is true.
A
6) 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.
A
7) A truck has four times the mass of a car and is moving with twice the speed of the car. If Kt and Kc refer to the kinetic energies of truck and car respectively, it is correct to say that A) Kt = 16Kc. B) Kt = 4Kc. C) Kt = 2Kc. D) Kt = Kc. E) Kt = Kc.
A
8) Three cars (car F, car G, and car H) are moving with the same speed and slam on their brakes. The most massive car is car F, and the least massive is car H. If the tires of all three cars have identical coefficients of kinetic friction with the road surface, which car travels the longest distance to skid to a stop? A) They all travel the same distance in stopping. B) Car F C) Car G D) Car H
A
16) 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.
A,B,E
58) How do the escape speeds for two rockets, the first weighing 20 N and the second weighing 20,000 N compare? A) The escape speed for the lighter rocket is smaller than that for the heavier rocket. B) The escape speed for the lighter rocket is the same as that for the heavier rocket. C) The escape speed for the lighter rocket is greater than that for the heavier rocket.
B
34) A heavy sled and a light sled, both moving horizontally with the same speed, suddenly slide onto a rough patch of snow and eventually come to a stop. The coefficient of kinetic friction between the sleds and the rough snow is the same for both of them. Which of the following statements about these sleds are correct? (There could be more than one correct choice.) A) Both sleds will slide the same distance on the rough snow before stopping. B) The heavy sled will slide farther on the rough snow than the light sled. C) The light sled will slide farther on the rough snow than the heavy sled. D) The friction from the snow will do more negative work on the heavy sled than on the light sled. E) The friction from the snow will do the same amount of work on both sleds.
A,D
43) A 5-kg ball collides inelastically head-on with a 10-kg ball, which is initially stationary. Which of the following statements is true? (There could be more than one correct choice.) A) The magnitude of the change of velocity the 5-kg ball experiences is greater than that of the 10-kg ball. B) The magnitude of the change of velocity the 5-kg ball experiences is less than that of the 10-kg ball. C) The magnitude of the change of velocity the 5-kg ball experiences is equal to that of the 10-kg ball. D) The magnitude of the change of the momentum of the 5-kg ball is equal to the magnitude of the change of momentum of the 10-kg ball. E) Both balls lose all their momentum since the collision is inelastic.
A,D
49) If a quantity you calculated had units of kg ∙ m/s, what type of quantity could it be? (There could be more than one correct choice.) A) momentum B) kinetic energy C) work D) impulse E) force
A,D
12) Which requires more work, increasing a car's speed from 0 mph to 30 mph or from 50 mph to 60 mph? A) 0 mph to 30 mph B) 50 mph to 60 mph C) It is the same in both cases.
B
15) The graphs shown show the magnitude F of the force exerted by a spring as a function of the distance x the spring has been stretched. For which one of the graphs does the spring obey Hooke's law? (PICTURE) A) Graph a B) Graph b C) Graph c D) Graph d E) Graph e
B
19) When you drop a pebble from height H, it reaches the ground with kinetic energy K if there is no air resistance. From what height should you drop it so it will reach the ground with twice as much kinetic energy? A) H B) 2H C) 4H D) 8H E) 16H
B
20) Two objects, one of mass m and the other of mass 2m, are dropped from the top of a building. If there is no air resistance, when they hit the ground A) both will have the same kinetic energy. B) the heavier one will have twice the kinetic energy of the lighter one. C) the heavier one will have four times the kinetic energy of the lighter one. D) the heavier one will have half the kinetic energy of the lighter one. E) the heavier one will have one-fourth the kinetic energy of the lighter one.
B
36) If a stone is dropped with an initial gravitational potential energy of 100 J but reaches the ground with a kinetic energy of only 75 J, this is a violation of the principle of conservation of energy. A) True B) False
B
44) In a game of pool, the white cue ball hits the #5 ball and stops, while the #5 ball moves away with the same velocity as the cue ball had originally. Both balls have the same mass. This type of collision is A) somewhat inelastic. B) elastic. C) completely inelastic.
B
50) A railroad car collides with and sticks to an identical railroad car that is initially at rest. After the collision, the kinetic energy of the system A) is the same as before. B) is half as much as before. C) is one third as much as before. D) is one fourth as much as before. E) is one quarter as much as before.
B
54) Two objects of different masses have momentum of equal, non-zero magnitude. Which object has more kinetic energy? A) the heavier object B) the lighter object C) They both have the same kinetic energy.
B
9) Three cars (car L, car M, and car N) are moving with the same speed and slam on their brakes. The most massive car is car L, and the least massive is car N. If the tires of all three cars have identical coefficients of kinetic friction with the road surface, for which car is the amount of work done by friction in stopping it the greatest? A) The amount of work done by friction is the same for all cars. B) Car L C) Car M D) Car N
B
32) A 1-kg ball is released from a height of 6 m, and a 2-kg ball is released from a height of 3 m. Air resistance is negligible as they fall. Which of the following statements about these balls are correct? (There could be more than one correct choice.) A) As they reach the ground, the 1-kg ball will have more kinetic energy than the 2-kg ball because it was dropped from a greater height. B) As they reach the ground, the 1-kg ball will be moving faster than the 2-kg ball. C) Both balls will reach the ground with the same speed. D) Both balls will reach the ground with the same kinetic energy. E) Both balls will take the same time to reach the ground.
B,D
33) A heavy dart and a light dart are launched vertically by identical ideal springs. Both springs were initially compressed by the same amount. There is no significant air resistance. Which of the following statements about these darts are correct? (There could be more than one correct choice.) A) The heavy dart goes higher than the light dart. B) The light dart goes higher than the heavy dart. C) Both darts reach the same maximum height. D) At the maximum height, both darts have the same gravitational potential energy. E) Both darts began moving upward with the same initial speed.
B,D
30) A heavy rock and a light rock are dropped from the same height and experience no significant air resistance as they fall. Which of the following statements about these rocks are correct? (There could be more than one correct choice.) A) Both rocks have the same kinetic energy when they reach the ground. B) Both rocks have the same speed when they reach the ground. C) The heavier rock reaches the ground before the lighter rock. D) Just as they were released, both rocks had the same amount of gravitational potential energy. E) When they reach the ground, the heavier rock has more kinetic energy than the lighter rock.
B,E
28) A heavy frog and a light frog jump straight up into the air. They push off in such away that they both have the same kinetic energy just as they leave the ground. Air resistance is negligible. Which of the following statements about these frogs are correct? (There could be more than one correct choice.) A) Just as they leave the ground, the heavier frog is moving faster than the lighter frog. B) Just as they leave the ground, the lighter frog is moving faster than the heavier frog. C) They both leave the ground with the same speed. D) The lighter frog goes higher than the heavier frog. E) The heavier frog goes higher than the lighter frog. F) Both frogs reach the same maximum height.
B,F
18) When you drop a pebble from height H, it reaches the ground with speed V if there is no air resistance. From what height should you drop it so it will reach the ground with twice speed? A) H B) 2H C) 4H D) 8H E) 16H
C
21) Swimmers at a water park have a choice of two frictionless water slides, as shown in the figure. Although both slides drop over the same height h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the bottom of slide 1 compare with v2, the speed of a swimmer reaching the end of slide 2? (PICTURE) A) v1 > v2 B) v1 < v2 C) v1 = v2 D) The heavier swimmer will have a greater speed than the lighter swimmer, no matter which slide he uses. E) No simple relationship exists between v1 and v2.
C
3) If the force on an object is in the negative direction, the work it does on the object must be A) negative. B) positive. C) The work could be either positive or negative, depending on the direction the object moves.
C
41) The momentum of an isolated system is conserved A) only in inelastic collisions. B) only in elastic collisions. C) in both elastic and inelastic collisions.
C
47) In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after, are shown. The collision is (PICTURE) A) perfectly elastic. B) partially inelastic. C) completely inelastic. D) characterized by an increase in kinetic energy. E) not possible because momentum is not conserved.
C
5) You throw a baseball straight up. Compare the sign of the work done by gravity while the ball goes up with the sign of the work done by gravity while it goes down. A) The work is positive on the way up and positive on the way down. B) The work is positive on the way up and negative on the way down. C) The work is negative on the way up and positive on the way down. D) The work is negative on the way up and on the way down because gravity is always downward.
C
29) 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. 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.
C,D,E
35) A heavy sled and a light sled, both moving horizontally with the same kinetic energy, suddenly slide onto a rough patch of snow and eventually come to a stop. The coefficient of kinetic friction between the sleds and the rough snow is the same for both of them. Which of the following statements about these sleds are correct? (There could be more than one correct choice.) A) Both sleds will slide the same distance on the rough snow before stopping. B) The heavy sled will slide farther on the rough snow than the light sled. C) The light sled will slide farther on the rough snow than the heavy sled. D) On the rough snow, the change in kinetic energy will be the same for both sleds. E) The friction from the snow will do the same amount of work on both sleds.
C,D,E
14) 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.
D
24) A person stands on the edge of a cliff. She throws three identical rocks with the same speed. Rock X is thrown vertically upward, rock Y is thrown horizontally, and rock Z is thrown vertically downward. If the ground at the base of the cliff is level, which rock hits the ground with the greatest speed if there is no air resistance? A) Rock X B) Rock Y C) Rock Z D) They all hit the ground with the same speed.
D
26) 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? (PICTURE) A) Ramp X B) Ramp Y C) Ramp Z D) The speed of the ball will be the same for all ramps.
D
37) If the units of your answer are kg ∙ m2/s3, which of the following types of quantities could your answer be? (There could be more than one correct choice.) A) kinetic energy B) potential energy C) force D) power E) work
D
4) 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
D
48) An egg falls from a bird's nest in a tree and feels no effects due to the air. As it falls, A) only its kinetic energy is conserved. B) only its momentum is conserved. C) both its kinetic energy and its momentum are conserved. D) only its mechanical energy is conserved. E) both its mechanical energy and its momentum are conserved.
D
56) If you want to double the momentum of a gas molecule, by what factor must you increase its kinetic energy? A) B) 2 C) 2 D) 4 E) 16
D
2) Two men, Joel and Jerry, push against a car that has stalled, trying unsuccessfully to get it moving. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do on the car. A) Joel does 75% more work than Jerry. B) Joel does 50% more work than Jerry. C) Jerry does 50% more work than Joel. D) Joel does 25% more work than Jerry. E) Neither of them does any work.
E
27) A girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case. Case A: Thrown straight up. Case B: Thrown straight down. Case C: Thrown out at an angle of 45° above horizontal. Case D: Thrown straight out horizontally. In which case will the speed of the stone be greatest when it hits the water below if there is no significant air resistance? A) Case A B) Case B C) Case C D) Case D E) The speed will be the same in all cases.
E
39) Jill does twice as much work as Jack does and in half the time. Jill's power output is A) the same as Jack's power output. B) one-fourth as much as Jack's power output. C) one-half as much as Jack's power output. D) twice Jack's power output. E) four times Jack's power output.
E
46) In the figure showing an isolated system, determine the character of the collision. The masses of the blocks, and the velocities before and after, are shown. The collision is (PICTURE) A) perfectly elastic. B) partially inelastic. C) completely inelastic. D) characterized by an increase in kinetic energy. E) not possible because momentum is not conserved
E
59) Planet A has twice the mass of Planet B. From this information, what can we conclude about the escape speed for Planet A compared to that of Planet B? A) The escape speed for Planet A must be twice as great as the escape speed from Planet B. B) The escape speed for Planet A must be four times as great as the escape speed from Planet B. C) The escape speed for Planet A is the same as the escape speed from Planet B. D) The escape speed for Planet A is greater than the escape speed from Planet B, but we cannot say how much greater. E) We cannot conclude anything about the escape speed for Planet A without knowing the radii of the two planets.
E