Physics for Scientists and Engineers, 3e (Knight)Chapter 10 Energy

10.1 Conceptual Questions

1) Consider a plot of the displacement (x) as a function of the applied force (F) for an ideal elastic spring. The slope of the curve would beA) the spring constant.B) the reciprocal of the spring constant.C) the acceleration due to gravity.D) the reciprocal of the acceleration of gravity.E) the mass of the object attached to the spring.Answer: BVar: 1

2) Which of the graphs in the figure illustrates Hooke's Law?

A) Graph aB) Graph bC) Graph cD) graph dAnswer: BVar: 1

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) Which of the graphs in the figure represents a spring that gets less stiff the more it is stretched?

A) Graph aB) Graph bC) Graph cD) Graph dAnswer: DVar: 1

4) Is it possible for a system to have negative potential energy?A) Yes, as long as the kinetic energy is positive.B) Yes, as long as the total energy is positive.C) Yes, since the choice of the zero of potential energy is arbitrary.D) No, because the kinetic energy of a system must equal its potential energy.E) No, because this would have no physical meaning.Answer: CVar: 1

5) On a smooth horizontal floor, an object slides into a spring which is attached to another mass that is initially stationary. When the spring is most compressed, both objects are moving at the same speed. Ignoring friction, what is conserved during this interaction?A) momentum and mechanical energyB) momentum onlyC) kinetic energy onlyD) momentum and kinetic energyE) momentum and potential energyAnswer: AVar: 1

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6) A baseball is thrown vertically upward and feels no air resistance. As it is risingA) both its momentum and its mechanical energy are conserved.B) its momentum is not conserved, but its mechanical energy is conserved.C) both its momentum and its kinetic energy are conserved.D) its kinetic energy is conserved, but its momentum is not conserved.E) its gravitational potential energy is not conserved, buts its momentum is conserved.Answer: BVar: 1

7) In a perfectly ELASTIC collision between two perfectly rigid objectsA) the momentum of each object is conserved.B) the kinetic energy of each object is conserved.C) the momentum of the system is conserved but the kinetic energy of the system is not conserved.D) both the momentum and the kinetic energy of the system are conserved.E) the kinetic energy of the system is conserved, but the momentum of the system is not conserved.Answer: DVar: 1

8) In an INELASTIC collision between two objectsA) the momentum of each object is conserved.B) the kinetic energy of each object is conserved.C) the momentum of the system is conserved but the kinetic energy of the system is not conserved.D) both the momentum and the kinetic energy of the system are conserved.E) the kinetic energy of the system is conserved, but the momentum of the system is not conserved.Answer: CVar: 1

9) A shell explodes into two fragments, one fragment 25 times heavier than the other. If any gas from the explosion has negligible mass, thenA) the momentum change of the lighter fragment is 25 times as great as the momentum change of the heavier fragment.B) the momentum change of the heavier fragment is 25 times as great as the momentum change of the lighter fragment.C) the momentum change of the lighter fragment is exactly the same as the momentum change of the heavier fragment.D) the kinetic energy change of the heavier fragment is 25 times as great as the kinetic energy change of the lighter fragment.E) the kinetic energy change of the lighter fragment is 25 times as great as the kinetic energy change of the heavier fragment.Answer: CVar: 1

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10) Jacques and George meet in the middle of a lake while paddling in their canoes. They come to a complete stop and talk for a while. When they are ready to leave, Jacques pushes George's canoe with a

force to separate the two canoes. What is correct to say about the final momentum and kinetic energy

of the system if we can neglect any resistance due to the water?

A) The final momentum is in the direction of but the final kinetic energy is zero.

B) The final momentum is in the direction opposite of but the final kinetic energy is zero.

C) The final momentum is in the direction of and the final kinetic energy is positive.

D) The final momentum is zero and the final kinetic energy is zero.E) The final momentum is zero but the final kinetic energy is positive.Answer: BVar: 1

11) A 1.0-kg block and a 2.0-kg block are pressed together on a horizontal frictionless surface with a compressed very light spring between them. They are not attached to the spring. After they are released and have both moved free of the springA) the lighter block will have more kinetic energy than the heavier block.B) the heavier block will have more kinetic energy than the lighter block.C) both blocks will both have the same amount of kinetic energy.D) both blocks will have equal speeds.E) the magnitude of the momentum of the heavier block will be greater than the magnitude of the momentum of the lighter block.Answer: AVar: 1

10.2 Problems

1) A spring stretches by 21.0 cm when a 135 N object is attached. What is the weight of a fish that would stretch the spring by 31 cm?A) 199 NB) 91.0 NC) 145 ND) 279 NAnswer: AVar: 50+

2) An object attached to an ideal massless spring is pulled across a frictionless surface. If the spring

constant is 45 N/m and the spring is stretched by 0.88 m when the object is accelerating at 2.0 m/s2, what is the mass of the object?A) 20 kgB) 17 kgC) 22 kgD) 26 kgAnswer: AVar: 18

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3) In the figure, two identical ideal massless springs have unstretched lengths of 0.25 m and spring constants of 700 N/m. The springs are attached to a small cube and stretched to a length L of 0.30 m as in Figure A. An external force P pulls the cube a distance D = 0.020 m to the right and holds it there. (See Figure B.) The external force P, that holds the cube in place in Figure B, is closest to

A) 28 N.B) 25 N.C) 21 N.D) 18 N.E) 14 N.Answer: AVar: 1

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4) Block A (0.40 kg) and block B (0.30 kg) are on a frictionless table (see figure). Spring 1 connects block A to a frictionless peg at 0 and spring 2 connects block A and block B. When the blocks are in uniform circular motion about 0, the springs have lengths of 0.60 m and 0.40 m, as shown. The springs are ideal and massless, and the linear speed of block B is 2.0 m/s. If the distance that spring 2 stretches is 0.060 m, the spring constant of spring 2 is closest to

A) 18 N/m.B) 20 N/m.C) 22 N/m.D) 24 N/m.E) 26 N/m.Answer: BVar: 1

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5) Block A (0.40 kg) and block B (0.30 kg) are on a frictionless table (see figure). Spring 1 connects block A to a frictionless peg at 0 and spring 2 connects block A and block B. When the blocks are in uniform circular motion about 0, the springs have lengths of 0.60 m and 0.40 m, as shown. The springs are ideal and massless, and the linear speed of block B is 2.0 m/s. If the spring constant of spring 1 is equal to 30 N/m, the unstretched length of spring 1 is closest to

A) 0.51 m.B) 0.52 m.C) 0.53 m.D) 0.54 m.E) 0.55 m.Answer: CVar: 1

6) A force on a particle depends on position such that F(x) = (3.00 N/m2)x2 + (6.00 N/m)x for a particle constrained to move along the x-axis. What work is done by this force on a particle that moves from x = 0.00 m to x = 2.00 m?A) 10.0 JB) 20.0 JC) -48.0 JD) 24.0 JE) 48.0 JAnswer: BVar: 5

7) A person pushes horizontally on a heavy box and slides it across the level floor at constant velocity. The person pushes with a 60.0 N force for the first 6.88 m, at which time he begins to tire. The force he exerts then starts to decrease linearly from 60.0 N to 0.00 N across the remaining 6.88 m. How much total work did the person do on the box?A) 619 JB) 826 JC) 495 JD) 925 JAnswer: AVar: 50+

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8) It requires 49 J of work to stretch an ideal very light spring from a length of 1.4 m to a length of 2.9 m. What is the value of the spring constant of this spring?A) 15 N/mB) 44 N/mC) 29 N/mD) 22 N/mAnswer: AVar: 50+

9) A force F = bx3 acts in the x direction, where the value of b is 3.7 N/m3. How much work is done by this force in moving an object from x = 0.00 m to x = 2.6 m?A) 42 JB) 13 JC) 50 JD) 57 JAnswer: AVar: 13

10) In the figure, two identical springs have unstretched lengths of 0.25 m and spring constants of 300 N/m. The springs are attached to a small cube and stretched to a length L of 0.36 m as in Figure A. An external force P pulls the cube a distance D = 0.020 m to the right and holds it there. (See Figure B.) The work done by the external force P in pulling the cube 0.020 m is closest to

A) 0.12 J.B) 0.060 J.C) 6.0 J.D) 12 J.E) 0.80 J.Answer: AVar: 1

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11) A 1000.0 kg car is moving at 15 km/h. If a 2000.0 kg truck has 18 times the kinetic energy of the car, how fast is the truck moving?A) 45 km/hB) 63 km/hC) 54 km/hD) 36 km/hAnswer: AVar: 50+

12) How much energy is 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 MJB) 10.0 kJC) 20.0 kJD) 40.0 kJE) 0.960 MJAnswer: AVar: 1

13) The coefficient of the restitution of an object is defined as the ratio of its outgoing to incoming speed when the object collides with a rigid surface. For an object with a coefficient of 0.78, what fraction of the object's kinetic energy is lost during a single collision?A) 39%B) 16%C) 47%D) 61%Answer: AVar: 31

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14) An 8.0-kg block is released from rest, with v1 = 0.00 m/s, on a rough incline, as shown in the figure. The block moves a distance of 1.6-m down the incline, in a time interval of 0.80 s, and acquires a velocity of v2 = 4.0 m/s. How much work does gravity do on the block during this process?

A) +81 JB) +100 JC) +120 JD) -81 JE) -100 JAnswer: AVar: 1

15) You do 174 J of work while pulling your sister back on a swing, whose chain is 5.10 m long. You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest. What is your sister's mass, assuming negligible friction?A) 22.9 kgB) 19.5 kgC) 26.3 kgD) 28.4 kgAnswer: AVar: 50+

16) An athlete stretches a spring an extra 40.0 cm beyond its initial length. How much energy has he transferred to the spring, if the spring constant is 52.9 N/cm?A) 423 JB) 4230 kJC) 423 kJD) 4230 JAnswer: AVar: 50+

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17) A tennis ball bounces on the floor three times. If each time it loses 22.0% of its energy due to heating, how high does it rise after the third bounce, provided we released it 2.3 m from the floor?A) 110 cmB) 11 cmC) 110 mmD) 140 cmAnswer: AVar: 50+

18) A 0.500-kg ball traveling horizontally on a frictionless surface approaches a very massive stone at 20.0 m/s perpendicular to wall and rebounds with 70.0% of its initial kinetic energy. What is the magnitude of the change in momentum of the stone?A) 18.4 kg∙m/sB) 14.0 kg∙m/sC) 3.00 kg∙m/sD) 1.63 kg∙m/sE) 0.000 kg∙m/sAnswer: AVar: 5

19) A 620-g object traveling at 2.1 m/s collides head-on with a 320-g object traveling in the opposite direction at 3.8 m/s. If the collision is perfectly elastic, what is the change in the kinetic energy of the 620-g object?A) It loses 0.23 J.B) It gains 0.69 J.C) It loses 0.47 J.D) It loses 1.4 J.E) It doesn’t lose any kinetic energy because the collision is elastic.Answer: AVar: 1

20) A 2.3-kg object traveling at 6.1 m/s collides head-on with a 3.5-kg object traveling in the opposite direction at 4.8 m/s. If the collision is perfectly elastic, what is the final speed of the 2.3-kg object?A) 0.48 m/sB) 7.1 m/sC) 3.8 m/sD) 4.3 m/sE) 6.6 m/sAnswer: BVar: 1

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21) A car of mass 1689 kg collides head-on with a parked truck of mass 2000 kg. Spring mounted bumpers ensure that the collision is essentially elastic. If the velocity of the truck is 17 km/h (in the same direction as the car's initial velocity) after the collision, what was the initial speed of the car?A) 19 km/hB) 38 km/hC) 29 km/hD) 10 km/hAnswer: AVar: 50+

22) A block of mass m = 8.40 kg, moving on a horizontal frictionless surface with a speed 4.20 m/s, makes a perfectly elastic collision with a block of mass M at rest. After the collision, the 8.40 block recoils with a speed of 0.400 m/s. In the figure, the blocks are in contact for 0.200 s. The magnitude of the average force on the 8.40-kg block, while the two blocks are in contact, is closest to

A) 193 NB) 185 NC) 176 ND) 168 NE) 160 NAnswer: AVar: 1

23) A billiard ball traveling at 3.00 m/s collides perfectly elastically with an identical billiard ball initially at rest on the level table. The initially moving billiard ball deflects 30.0° from its original direction. What is the speed of the initially stationary billiard ball after the collision?A) 2.00 m/sB) 0.866 m/sC) 1.50 m/sD) 2.59 m/sE) 0.750 m/sAnswer: CVar: 1

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24) A pool player is attempting a fancy shot. He hits the cue ball giving it a speed of 5.57 m/s and directs its center on a path tangent to the surface of the target ball having the same mass as the cue ball. After the collision (on a frictionless table) the initially-stationary ball moves with a speed of 4.82 m/s. After the collision, the new speed of the cue ball and the relative direction of the balls are closest toA) 2.79 m/s, at 90° to each other.B) 2.79 m/s, at 60° to each other.C) 8.34 m/s, at 90° to each other.D) 8.34 m/s, at 60° to each other.Answer: AVar: 1

25) A 2.00-kg object traveling east at 20.0 m/s collides with a 3.00-kg object traveling west at 10.0 m/s. After the collision, the 2.00-kg object has a velocity 5.00 m/s to the west. How much kinetic energy was lost during the collision?A) 0.000 JB) 458 JC) 516 JD) 91.7 JE) 175 JAnswer: BVar: 1

26) A 15-g bullet is shot vertically into an 2-kg block. The block lifts upward 8.0 mm (see the figure). The bullet penetrates the block and comes to rest in it in a time interval of 0.0010 s. Assume the force on the bullet is constant during penetration and that air resistance is negligible. The initial kinetic energy of the bullet is closest to

A) 21 JB) 14 JC) 10 JD) 0.0012 JE) 0.16 JAnswer: AVar: 50+

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27) An 8.0-g bullet is shot into a 4.0-kg block, at rest on a frictionless horizontal surface (see the figure). The bullet remains lodged in the block. The block moves into an ideal massless spring and compresses it by 8.7 cm. The spring constant of the spring is 2400 N/m. The initial velocity of the bullet is closest to

A) 1100 m/s.B) 1200 m/s.C) 900 m/s.D) 1300 m/s.E) 1000 m/s.Answer: AVar: 1

28) In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after are given. The collision is

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.Answer: AVar: 1

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29) In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after are given, and no other unbalanced forces act on these blocks. The collision is

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.Answer: EVar: 1

30) A 5.00-kg ball is hanging from a long but very light flexible wire when it is struck by a 1.50-kg stone traveling horizontally to the right at 12.0 m/s. The stone rebounds to the left with a speed of 8.50 m/s, and the ball swings to a maximum height h above its original level. The value of h is closest toA) 0.0563 m.B) 1.10 m.C) 1.93 m.D) 2.20 m.E) 3.69 m.Answer: CVar: 1

31) On a frictionless horizontal table, two blocks (A of mass 2.00 kg and B of mass 3.00 kg) are pressed together against an ideal massless spring that stores 75.0 J of elastic potential energy. The blocks are not attached to the spring and are free to move free of it once they are released from rest. The maximum speed achieved by each block is closest to:A) 6.71 m/s (A), 4.47 m/s (B)B) 4.47 m/s (A), 6.71 m/s (B)C) 5.48 m/s for bothD) 6.12 m/s (A), 5.00 m/s (B)E) 5.00 m/s (A), 6.12 m/s (B)Answer: AVar: 1

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32) A 10.0-kg shell is traveling horizontally to the right at 25.0 m/s relative to the ground when it explodes into two fragments, one of mass 3.00 kg and the other of mass 7.00 kg. The lighter fragment goes directly forward, and the explosion releases 1.50 × 103 J of mechanical energy to the fragments. Find the magnitude and direction of the velocity of the heavier fragment relative to the ground just after the explosion. Ignore the effect of any ejected gases.Answer: 13.7 m/s to the rightVar: 1

33) A 1.2-kg spring-activated toy bomb slides on a smooth surface along the x-axis with a speed of 0.50 m/s. At the origin 0, the bomb explodes into two fragments. Fragment 1 has a mass of 0.40 kg and a speed of 0.90 m/s along the negative y-axis. In the figure, the energy released by the explosion is closest to

A) 0.20 J.B) 0.24 J.C) 0.28 J.D) 0.32 J.E) 0.36 J.Answer: DVar: 1

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