Physics Chapter 6
A
35) How much work must be done by frictional forces in slowing a 1000-kg car from to rest? A) 3.41 × 105 J B) 2.73 × 105 J C) 4.09 × 105 J D) 4.77 × 105 J
E
56) An ideal spring has a spring constant (force constant) of 2500 N/m. is stretched 4.0 cm. How much work is required to stretch the spring by 4.0 cm? A) 4.0 J B) 0.00 J C) 1.0 J D) 3.0 J E) 2.0 J
3.2 × 106 m/m
57) 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?
3.5 cm
6) A very light ideal spring having a spring constant (force constant) of 8.2 N/cm is used to lift a 2.2-kg tool with an upward acceleration of 3.25 m/s2. If the spring has negligible length when it us not stretched, how long is it while it is pulling the tool upward?
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
63) 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
A
64) An ideal spring with a spring constant (force constant) of is stretched from equilibrium to 2.9 m. How much work is done in the process? A) 93 J B) 186 J C) 47 J D) 121 J
E
80) A small but dense 2.0-kg stone is attached to one end of a very light rod that is 1.2 m long. The other end of the rod is attached to a frictionless pivot. The rod is raised until it is vertical, with the stone above the pivot. The rod is released and the stone moves in a vertical circle with no air resistance. What is the tension in the rod as the stone moves through the bottom of the circle? A) 20 N B) 40 N C) 60 N D) 80 N E) 100 N
A
10) A child does 350 J of work while pulling a box from the ground up to his tree house at a steady speed with a light rope. The tree house is above the ground. What is the mass of the box? A) 8.9 kg B) 5.3 kg C) 6.7 kg D) 8.0 kg
A
11) You carry a 7.0-kg bag of groceries above the ground at constant speed across a room. How much work do you do on the bag in the process? A) 0.00 J B) 82 J C) 185 J D) 157 J
A
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.
D
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.
B
16) A 30-N box is pulled upward 6.0 m along the surface of a ramp that rises at 37° above the horizontal. How much work does gravity do on the box during this process? A) -1100 J B) -110 J C) -140 J D) -180 J E) 120 J
A, B, E
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.
E
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
A
18) Find the net work done by friction on a box that moves in a complete circle of radius on a uniform horizontal floor. The coefficient of kinetic friction between the floor and the box is 0.25, and the box weighs A) 190 J B) 0 J C) 1800 J D) 370 J
C
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
-59 J
19) 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?
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
A
2) A force of stretches a very light ideal spring from equilibrium. What is the force constant (spring constant) of the spring? A) 41 N/m B) 22 N/m C) 34 N/m D) 46 N/m
E
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.
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
21) 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
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? 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
22) A stone with a mass of 1.0 kg is tied to the end of a light string which keeps it moving in a circle with a constant speed of 4.0 m/s on a perfectly smooth horizontal tabletop. The radius of the path is 0.60 m. How much work does the tension in the string do on the stone as it makes one-half of a complete circle? A) 100 J B) 3.8 J C) 0 J D) 40 J E) 80 J
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.
A
23) A force acts on an object, causing it to move parallel to the force. The graph in the figure shows this force as a function of the position of the object. How much work does the force do as the object moves from 4 m to 6 m? A) 20 J B) 30 J C) 0 J D) 40 J E) 70 J
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.
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.
B
25) A force acts on an object, causing it to move parallel to the force. The graph in the figure shows this force as a function of the position of the object. How much work does the force do as the object moves from 6 m to 12 m? A) 20 J B) 30 J C) 0 J D) 40 J E) 70 J
D
26) A force acts on an object, causing it to move parallel to the force. The graph in the figure shows this force as a function of the position of the object. How much work does the force do as the object moves from 0 to 15 m? A) 25 J B) 50 J C) 100 J D) 125 J E) 150 J
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? A) Ramp X B) Ramp Y C) Ramp Z D) The speed of the ball will be the same for all ramps.
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
28) The resultant force on an object over a 0.50-s time interval is plotted in the graph in the figure. How much work did this force do on the object during the 0.50-s interval? A) -25 J B) 50 J C) 22 J D) 12.5 J E) 0 J
7.1 m/s
29) How fast must a 6.0-kg cat run to have a kinetic energy of 150 J?
C, D, E
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.
A
3) A very light ideal spring stretches by when it is used to hang a 135-N object. What is the weight of a piece of electronic equipment that would stretch the spring by if you hung the equipment using the spring? A) 289 N B) 63 N C) 176 N D) 405 N
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.
B, E
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.
A, D, 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.
B
31) An object hits a wall and bounces back with half of its original speed. What is the ratio of the final kinetic energy to the initial kinetic energy of the object? A) 1/2 B) 1/4 C) 1/8 D) 1/16
B, D
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.
A
33) What is the minimum energy needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s? A) 1.10 MJ B) 10.0 kJ C) 20.0 kJ D) 40.0 kJ E) 0.960 MJ
C
34) A 1.0-kg object moving in a certain direction has a kinetic energy of 2.0 J. It hits a wall and comes back with half its original speed. What is the kinetic energy of this object at this point? A) 2.0 J B) 1.0 J C) 0.50 J D) 0.25 J E) 4.0 J
A, D
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.
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.
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
A
36) 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
D
37) A 10-kg dog is runnng with a speed of 5.0 m/s. What is the minimum work required to stop the dog in 2.40 s? A) 50 J B) 75 J C) 100 J D) 125 J
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
E
38) 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
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.
B
39) 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
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.
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
A
4) An object attached to a spring is pulled across a horizontal frictionless surface. If the force constant (spring constant) of the spring is 45 N/m and the spring is stretched by 0.88 m when the object is accelerating at what is the mass of the object? A) 28 kg B) 24 kg C) 31 kg D) 36 kg
A
40) 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
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
43) On an alien planet, an object moving at 4.0 m/s on the horizontal ground comes to rest after traveling a distance of 10 m. If the coefficient of kinetic friction between the object and the surface is 0.20, what is the value of g on that planet? A) 4.0 m/s2 B) 6.0 m/s2 C) 8.0 m/s2 D) 10 m/s2 E) 12 m/s2
C
45) The kinetic friction force that a horizontal surface exerts on a 60.0-kg object is 50.0 N. If the initial speed of the object is 25.0 m/s, what distance will it slide before coming to a stop? A) 15.0 m B) 30.0 m C) 375 m D) 750 m
D
46) A stone is moving on a rough level surface. It has 24 J of kinetic energy, and the friction force on it is a constant 0.50 N. What is the maximum distance it can slide? A) 2.0 m B) 12 m C) 24 m D) 48 m
A
47) In a ballistics test, a 28-g bullet pierces a sand bag that is thick. If the initial bullet velocity was and it emerged from the sandbag moving at what was the magnitude of the friction force (assuming it to be constant) that the bullet experienced while it traveled through the bag? A) 130 N B) 38 N C) 13 N D) 1.3 N
A
48) A certain car traveling at 34.0 mph skids to a stop in 29 meters from the point where the brakes were applied. In approximately what distance would the car have stopped had it been going 105.4 mph? A) 279 m B) 158 m C) 90 m D) 51 m E) 29 m
C
49) The horizontal force that an animal exerts on a large fruit it has found is observed and is shown in the graph in the figure. If the fruit was initially sliding on the frictionless ground at 5.5 cm/s when the animal first grabbed it, by how much did the animal change its kinetic energy during this encounter? A) 12.5 J B) 50 J C) 25 J D) 22 J E) 0 J
C
5) A 3.0-kg brick rests on a perfectly smooth ramp inclined at 34° above the horizontal. The brick is kept from sliding down the plane by an ideal spring that is aligned with the surface and attached to a wall above the brick. The spring has a spring constant (force constant) of 120 N/m. By how much does the spring stretch with the brick attached? A) 360 cm B) 240 cm C) 14 cm D) 24 cm E) 36 cm
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.
(a) +8.2 m/s (b) +2.0 m/s
50) The graph in the figure shows the magnitude of the net horizontal force Fx on a 25-kg package as a function of the position x of the package. Just before the force was applied, the package was originally sliding at 6.0 m/s in the +x direction on a smooth horizontal floor. Find the x component of the velocity of the package just after the force has stopped in each of the following cases. (a) The force is applied in the same direction as the original velocity of the box. (b) The force is applied in the opposite direction to the original velocity of the box.
A
52) You do 116 J of work while pulling your sister back on a fritctionless swing, whose chain is long, until the swing makes an angle of 32.0° with the vertical. What is your sister's mass? A) 15.3 kg B) 13.0 kg C) 17.6 kg D) 19.0 kg
A
53) A tennis ball bounces on the floor three times, and each time it loses 23.0% of its energy due to heating. How high does it bounce after the third time, if we released it from the floor? A) 180 cm B) 18 cm C) 180 mm D) 240 cm
A
55) An ideal spring stretches by 21.0 cm when a 135-N object is hung from it. If instead you hang a fish from this spring, what is the weight of a fish that would stretch the spring by A) 199 N B) 91 N C) 145 N D) 279 N
E
58) If 4.0 J of work are performed in stretching an ideal spring with a spring constant (force constant) of 2500 N/m, by what distance is the spring stretched? A) 3.2 cm B) 3.2 m C) 0.3 cm D) 5.7 m E) 5.7 cm
D
59) If the work done to stretch an ideal spring by 4.0 cm is 6.0 J, what is the spring constant (force constant) of this spring? A) 300 N/m B) 3000 N/m C) 3500 N/m D) 7500 N/m E) 6000 N/m
A
60) An ideal spring has a spring constant (force constant) of 60 N/m. How much energy does it store when it is stretched by 1.0 cm? A) 0.0030 J B) 0.30 J C) 60 J D) 600 J
(a) 46 cm (b) 32 cm (c) 32 cm
7) A very light ideal spring with a spring constant (force constant) of 2.5 N/cm pulls horizontally on an 18-kg box that is resting on a horizontal floor. The coefficient of static friction between the box and the floor is 0.65, and the coefficient of kinetic friction is 0.45. (a) How long is the spring just as the box is ready to move? (b) If the spring pulls the box along with a constant forward velocity of 1.75 m/s, how long is the spring? (c) How long is the spring if it pulls the box forward at a constant 2.75 m/s?
19 cm
8) A very light ideal spring of spring constant (force constant) 2.5 N/cm is 15 cm long when nothing is attached to it. It is now used to pull horizontally on a 12.5-kg box on a perfectly smooth horizontal floor. You observe that the box starts from rest and moves 96 cm during the first 1.6 s of its motion with constant acceleration. How long is the spring during this motion?
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
9) How much work would a child do while pulling a 12-kg wagon a distance of with a force? A) 95 J B) 52 J C) 67 J D) 109 J
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
D
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.
C
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.
D
100) A 1500-kg car accelerates from rest to 25 m/s in 7.0 s. What is the average power delivered by the engine? (1 hp = 746 W) A) 60 hp B) 70 hp C) 80 hp D) 90 hp
B
101) At what minimum rate is a 60.0-kg boy using energy when, in 8.00 s, he runs up a flight of stairs that is 10.0-m high? A) 75.0 W B) 735 W C) 4.80 kW D) 48.0 W
A
102) If electricity costs 7.06¢/kW∙h, how much would it cost you to run a stereo system per day for A) $0.95 B) $0.14 C) $1.62 D) $2.66
A
103) A 1321-kg car climbs a 5.0° slope at a constant speed of Assuming that air resistance may be neglected, at what rate (in kW) must the engine deliver energy to the drive wheels of the car? A) 25 kW B) 287 kW C) 38 kW D) 48 kW
920 km
104) A typical incandescent light bulb consumes 75 W of power and has a mass of 30 g. You want to save electrical energy by dropping the bulb from a height great enough so that the kinetic energy of the bulb when it reaches the floor will be the same as the energy it took to keep the bulb on for 1.0 hour. From what height should you drop the bulb, assuming no air resistance and constant g?
E
105) What is the net power needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s in 4.00 seconds? A) 100 kW B) 10.0 kW C) 140 kW D) 14.0 kW E) 275 kW
3.1 MW
106) Water flows over a waterfall that is 20 m high at the rate of 4.0 × 104 kg/s. If this water powers an electric generator with a 40% efficiency, how many watts of electric power can be supplied?
D
107) A certain battery charger uses 12 W of power. At 6.0 cents per kilowatt-hour, how much does it cost to charge batteries for a full day? A) 28¢ B) 1.4¢ C) 75¢ D) 1.7¢ E) 2.3¢
$4.03
108) A family goes on vacation for one week but forgets to turn off an electric fan that consumes electricity at the rate of 200 W. If the cost of electricity is 12.0¢/kW∙h how much does it cost (to the nearest penny) to run the fan for the week?
(a) $17 (b) 6.05 × 108 J
109) Suppose you left five 100-W light bulbs burning in the basement for two weeks. If electricity costs 10.0¢/kW∙h, (a) how much did the electricity cost (to the nearest dollar) to leave those bulbs on, and (b) how many joules of electrical energy did they consume?
(a) 6.3 kJ (b) 290 W (c) 0.39 hp
111) 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) (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?
D
112) A sand mover at a quarry lifts 2,000 kg of sand per minute a vertical distance of 12 m. The sand is initially at rest and is discharged at the top of the sand mover with speed 5.0 m/s into a loading chute. What minimum power must be supplied to this machine? A) 520 W B) 3.9 kW C) 6.7 kW D) 4.3 kW E) 1.1 kW
A
12) It requires 0.30 kJ of work to fully drive a stake into the ground. If the average resistive force on the stake by the ground is how long is the stake? A) 0.36 m B) 0.23 m C) 0.31 m D) 0.41 m
B
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.
A
13) A crane lifts a 425 kg steel beam vertically upward a distance of How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s2? Neglect frictional forces. A) 4.7 × 105 J B) 2.7 × 105J C) 3.2 × 105 J D) 4.0 × 105 J
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.
A
14) 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
(a) 275 Kj (b) -245 kJ (c) 30.0 kJ
15) 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?
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? A) Graph a B) Graph b C) Graph c D) Graph d E) Graph e
E
20) A person carries a 25.0-N rock through the path shown in the figure, starting at point A and ending at point B. The total time from A to B is 1.50 min. How much work did gravity do on the rock between A and B? A) 625 J B) 20.0 J C) 275 J D) 75 J E) 0 J
A
24) A force acts on an object, causing it to move parallel to the force. The graph in the figure shows this force as a function of the position of the object. How much work does the force do as the object moves from 0 m to 4 m? A) 20 J B) 30 J C) 0 J D) 40 J E) 70 J
C
27) The net force that an animal exerts on a large piece of fruit it has found is observed and is shown in the graph in the figure. If the force is parallel to the motion of the fruit, how much work did the animal do during the encounter? A) 12.5 J B) 50 J C) 25 J D) 22 J E) 0 J
B, F
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.
A
30) 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
A
32) A 1000-kg car is moving at 15 km/h. If a 2000-kg truck has 23 times the kinetic energy of the car, how fast is the truck moving? A) 51 km/h B) 72 km/h C) 61 km/h D) 41 km/h
C
41) 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
B
42) 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 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
C
44) A driver, traveling at 22 m/s, slows down her 2000 kg truck to stop for a red light. What work is done on the truck by the friction force of the road? A) -2.2 × 104 J B) -4.4 × 104 J C) -4.8 × 105 J D) -9.7 × 105 J
14 m
51) How high a hill would a 75-kg hiker have to climb to increase her gravitational potential energy by 10,000 J?
A
61) How much work is required to stretch an ideal spring of spring constant (force constant) 40 N/m from x = 0.20 m to x = 0.25 m if the unstretched position is at x = 0.00 m? A) 0.45 J B) 0.80 J C) 1.3 J D) 0.050 J
D
62) An ideal spring with a force constant (spring constant) of 15 N/m is initially compressed by 3.0 cm from its uncompressed position. How much work is required to compress the spring an additional 4.0 cm? A) 0.0068 J B) 0.012 J C) 0.024 J D) 0.030 J
(a) 27 cm (b) 2.3 m/s
70) 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?
B
71) The figure shows a famous roller coaster ride. You can ignore friction. If the roller coaster 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
C
77) A 5.0-N projectile leaves the ground with a kinetic energy of 220 J. At the highest point in its trajectory, its kinetic energy is 120 J. To what vertical height, relative to its launch point, did it rise if there was no air resistance? A) 44 m B) 24 m C) 20 m D) 10 m E) It is impossible to determine the height without knowing the angle of launch.
C
78) In the figure, a ball hangs by a very light string. What is the minimum speed of the ball at the bottom of its swing (point B) in order for it to reach point A, which is 1.0 m above the bottom of the swing? A) 2.2 m/s B) 3.1 m/s C) 4.4 m/s D) 4.9 m/s
D
85) A small 1.4-N stone slides down a frictionless bowl, starting from rest at the rim. The bowl itself is a hemisphere of radius 75 cm. Just as the stone reaches the bottom of the bowl, how hard is the bowl pushing on it? A) 0.70 N B) 1.4 N C) 2.8 N D) 4.2 N E) 5.6 N
A
86) A 30-N stone is dropped from a height of 10 m and strikes the ground with a speed of 13 m/s. What average force of air friction acted on the stone as it fell? A) 4.1 N B) 2.9 N C) 0.13 kN D) 7.2 N E) 1.2 N
4.3 m/s
96) As shown in the figure, a 4.0-kg block is moving at 5.0 m/s along a horizontal frictionless surface toward an ideal spring that is attached to a wall. After the block collides with the spring, the spring is compressed a maximum distance of 0.68 m. What is the speed of the block when the spring is compressed to only one-half of the maximum distance?
5.4 MJ
97) How many joules of energy are used by a 2.0 hp motor that runs for 1.0 hour? (1 hp = 746 W)
A
98) A child pulls on a wagon with a force of If the wagon moves a total of in what is the average power delivered by the child? A) 17 W B) 21 W C) 22 W D) 26 W
B
99) How many joules of energy are used by a 1.0-hp motor that runs for 1.0 hour? (1 hp = 746 W) A) 3.6 kJ B) 2.7 MJ C) 45 kJ D) 4.8 J
B
1) An ornament of mass 40.0 g is attached to a vertical ideal spring with a force constant (spring constant) of 20.0 N/m. The ornament is then lowered very slowly until the spring stops stretching. How much does the spring stretch? A) 0.00200 m B) 0.0196 m C) 0.0816 m D) 0.800 m E) 0.200 m
C
17) Matthew pulls his little sister Sarah along the horizontal ground in a wagon. He exerts a force on the wagon of 60.0 N at an angle of 37.0° above the horizontal. If he pulls her a distance of 12.0 m, how much work does Matthew do? A) 185 J B) 433 J C) 575 J D) 720 J
(a) 0.25 Kj (b) 0.12 kW (c) the same work, but the power doubles
110) 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 s
113) A 100%-efficient engine is being used to raise a 89-kg crate vertically upward at a steady rate. If the power output of the engine is 1620 W, how long does it take the engine to lift the crate a vertical distance of 18.7 m? Friction in the system is negligible.
C
114) The net force that an animal exerts on a large fruit it has found is observed over a 10-s interval and is shown in the graph in the figure. What was the average power delivered to the fruit by the animal over this time interval? A) 0.00 W B) 1.3 W C) 2.5 W D) 2.2 W E) 5.0 W
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.
B
54) A 10-kg mass, hung by an ideal spring, causes the spring to stretch 2.0 cm. What is the spring constant (force constant) for this spring? A) 5.0 N/cm B) 49 N/cm C) 0.20 N/cm D) 20 N/m E) 0.0020 N/cm
C
65) 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
A
66) 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
A
67) A prankster drops a water balloon from the top of a building. If the balloon is traveling at 29.1 m/s when it strikes a window ledge that is 1.5 m above the ground, how tall is the building? Neglect air resistance. A) 45 m B) 43 m C) 46 m D) 47 m
A
68) A spring-loaded dart gun is used to shoot a dart straight up into the air, and the dart reaches a maximum height of 24 meters. The same dart is shot up a second time from the same gun, but this time the spring is compressed only half as far (compared to the first shot). How far up does the dart go this time (neglect all friction and assume the spring is ideal)? A) 6.0 m B) 12 m C) 3.0 m D) 48 m
B
69) 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.
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.
C
72) What is the minimum energy needed to lift a 1.0-kg rocket to a height of 200 km and to give it a speed of 8.0 km/s at that height? (Neglect air resistance and the small decrease in g over that distance.) A) 34 TJ B) 34 kJ C) 34 MJ D) 34 GJ E) 34 J
A
73) Assuming negligible friction, what spring constant (force constant) would be needed by the spring in a "B-B gun" to fire a 10-g pellet to a height of 100 m if the spring is initially compressed by 0.10 m? A) 20 N/cm B) 20 N/m C) 200 N/m D) 2000 N/cm E) 0.0020 N/m
E
74) If a spring-operated gun can shoot a pellet to a maximum height of 100 m on Earth, how high could the pellet rise if fired on the Moon, where g = 1.6 m/s2? A) 17 m B) 160 m C) 3.6 km D) 100 m E) 610 m
B
75) A 60-kg skier pushes off the top of a frictionless hill with an initial speed of 4.0 m/s. How fast will she be moving after dropping 10 m in elevation? Air resistance is negligible. A) 0.20 km/s B) 15 m/s C) 10 m/s D) 0.15 km/s E) 49 m/s
B
76) 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
D
79) A 1500-kg car moving at 25 m/s hits an initially uncompressed horizontal ideal spring with spring constant (force constant) of 2.0 × 106 N/m. What is the maximum distance the spring compresses? A) 0.17 m B) 0.34 m C) 0.51 m D) 0.68 m
D
81) In a museum exhibit of a simple pendulum, a very small but dense 6.0-kg ball swings from a very light 2.5-m wire. The ball is released from rest when the pendulum wire makes a 65° angle with the vertical, and it swings in a circular arc with no appreciable friction or air resistance. What is the tension in the wire just as the ball swings through its lowest position? A) 11 N B) 59 N C) 68 N D) 130 N E) 0 N
48 m
82) 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.
C
83) 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
B
84) A stone is released from rest at a height h at the left side of a loop-the-loop, as shown in the figure. There is no appreciable friction from the track or from air resistance. If the radius of the loop is R, what is the minimum height h for which the stone will not fall off the track at the top of the loop? A) 3.5 R B) 2.5 R C) 2.0 R D) R E) 3.0 R
C
87) A 60-kg skier starts from rest from the top of a 50-m high slope. If the work done by friction is -6.0 kJ, what is the speed of the skier on reaching the bottom of the slope? A) 17 m/s B) 24 m/s C) 28 m/s D) 31 m/s
160 J
88) 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 nonconservative forces on the hill?
D
89) An object with a mass of 10 kg is initially at rest at the top of a frictionless inclined plane that rises at 30° above the horizontal. At the top, the object is initially 8.0 m from the bottom of the incline, as shown in the figure. When the object is released from this position, it eventually stops at a distance d from the bottom of the inclined plane along a horizontal surface, as shown. The coefficient of kinetic friction between the horizontal surface and the object is 0.20, and air resistance is negligible. Find the distance d. A) 5.0 m B) 10 m C) 15 m D) 20 m E) 25 m
C
90) On a planet where g = 10.0 m/s2 and air resistance is negligible, a sled is at rest on a rough inclined hill rising at 30° as shown in the figure. The object is allowed to move and it stops on a rough horizontal surface, at a distance of 4.0 m from the bottom of the hill. The coefficient of kinetic friction on the hill is 0.40. What is the coefficient of kinetic friction between the horizontal surface and the sled? A) 0.10 B) 0.20 C) 0.31 D) 0.40 E) 0.60
A
91) A 0.12-kg block is held in place against the spring by a 35-N horizontal external force. The external force is removed, and the block is projected with a velocity when it separates from the spring, as shown in the figure. The block descends a ramp and has a velocity at the bottom of the ramp. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction between the block and the rough surface is 0.26. The block moves on to D, where it stops. By how many centimeters was the spring initially compressed? A) 0.49 cm B) 0.26 cm C) 0.18 cm D) 0.99 cm E) 0.67 cm
A
92) As shown in the figure, a 1.45-kg block is held in place against the spring by a 21-N horizontal external force. The external force is removed, and the block is projected with a velocity as it separates from the spring. The block descends a ramp and has a velocity at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction between the block and the rough surface is 0.29. The velocity of the block is at C. The block moves on to D, where it stops. How much work is done by friction between points B and C? A) -1.8 J B) -3.6 J C) -14 J D) -6.4 J E) -7.0 J
A
93) A 0.46-kg block is held in place against the spring by a 30-N horizontal external force. The external force is removed, and the block is projected with a velocity upon separation from the spring, as shown in the figure. The block descends a ramp and has a velocity at the bottom. The track is frictionless between points A and B. The block enters a rough section at point B, extending to E. The coefficient of kinetic friction between the block and the rough surface is 0.38. The velocity of the block is at point C. The block moves on to D, where it stops. What distance does the block travel between points B and D? A) 0.30 m B) 0.039 m C) 0.26 m D) 0.40 m E) 0.60 m
3.7 m
94) A sled is moving along a horizontal surface with a speed of 5.7 m/s. It then slides up a rough hill having a slope of 11° above the horizontal. The coefficient of kinetic friction between the sled and the surface of the hill is 0.26. How far along the surface does the block travel up the incline?
1.9 m/s
95) The figure shows two crates, each of mass m = 24 kg, that are connected by a very light wire. The coefficient of kinetic friction between the crate on the inclined surface and the surface itself is 0.31. Find the speed of the crates after they have moved 1.6 m starting from rest.
