Chapter 7

1) 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 J B) +100 J C) +120 J D) -81 J E) -100 J

A

2) 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 kg B) 19.5 kg C) 26.3 kg D) 28.4 kg

A

3) 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 J B) 4230 kJ C) 423 kJ D) 4230 J

A

4) 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 cm B) 11 cm C) 110 mm D) 140 cm

A

8) When an object is solely under the influence of conservative forces, the sum of its kinetic and potential energies does not change. A) True B) False

A

9) A ball drops some distance and gains 30 J of kinetic energy. Do NOT ignore air resistance. How much gravitational potential energy did the ball lose? A) more than 30 J B) exactly 30 J C) less than 30 J

A

14) A potential energy function for system 1 is given by U1(x) = Cx2 + Bx3. The potential energy function for system 2 is given by U2(x) = A + Cx2 + Bx3, where A is a positive quantity. How does the force on system 1 relate to the force on system 2 at a given position? A) The force on the two systems will be in opposite directions. B) The force is identical on the two systems. C) The force on the second system will be with less than the force on the first system. D) There is no relationship between the forces on the two systems. E) The force on the second system will be with greater than the force on the first system.

B

4) Two identical balls are thrown directly upward, ball A at speed v and ball B at speed 2v, and they feel no air resistance. Which statement about these balls is correct? A) Ball B will go twice as high as ball A because it had twice the initial speed. B) Ball B will go four times as high as ball A because it had four times the initial kinetic energy. C) The balls will reach the same height because they have the same mass and the same acceleration. D) At its highest point, ball B will have twice as much gravitational potential energy as ball A because it started out moving twice as fast. E) At their highest point, the acceleration of each ball is instantaneously equal to zero because they stop for an instant.

B

1) 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.

C

10) A ball drops some distance and loses 30 J of gravitational potential energy. Do NOT ignore air resistance. How much kinetic energy did the ball gain? A) more than 30 J B) exactly 30 J C) less than 30 J

C

37) A potential energy function is given by U(x) = ( 3.00 N/m)x - ( 1.00 N/m3)x3. At what position or positions is the force equal to zero? A) m and - m B) 0.00 m, m and - m C) 1.00 m and -1.00 m D) 3.00 m and -3.00 m E) The force is not zero at any location.

C

38) The potential energy for a certain mass moving in one dimension is given by U(x) = (2.0 J/m3)x3 - (15 J/m2)x2 + (36 J/m)x - 23 J. Find the location(s) where the force on the mass is zero. A) 4.0 m, 5.0 m B) 1.0 m C) 2.0 m, 3.0 m D) 3.0 m, 5.0 m

C

11) Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. If the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline? A) We must know the actual masses of the blocks to answer. B) Both blocks have the same speed at the bottom. C) Block 1 is faster. D) Block 2 is faster. E) There is not enough information to answer the question because we do not know the value of the coefficient of kinetic friction.

D

13) Which, if any, of the following statements concerning the work done by a conservative force is NOT true? A) It can always be expressed as the difference between the initial and final values of a potential energy function. B) It is independent of the path of the body and depends only on the starting and ending points. C) When the starting and ending points are the same, the total work is zero. D) All of the above statements are true. E) None of the above statements are true.

D

17) Consider the motion of a 1.00-kg particle that moves with potential energy given by U(x) = (-2.00 J∙m)/x + (4.00 J∙m2)/x2. Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m? A) 2.13 m/s B) 3.00 m/s C) 4.68 m/s D) 3.67 m/s

D

19) A projectile is fired from ground level at an angle of 40.0° above horizontal at a speed of 30.0 m/s. What is the speed of the projectile when it has reached a height equal to 50.0% of its maximum height? A) 26.0 m/s B) 27.4 m/s C) 28.7 m/s D) 26.7 m/s E) 28.1 m/s

D

20) A very small 100-g object is attached to one end of a massless 10-cm rod that is pivoted without friction about the opposite end. The rod is held vertical, with the object at the top, and released, allowing the rod to swing. What is the speed of the object at the instant that the rod is horizontal? A) 0.71 m/s B) 4.0 m/s C) 1.4 m/s D) 2.8 m/s E) 2.8 m/s

D

3) Two stones, one of mass m and the other of mass 2m, are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance. Which statement about these stones is true? A) The heavier stone will go twice as high as the lighter one because it initially had twice as much kinetic energy. B) Both stones will reach the same height because they initially had the same amount of kinetic energy. C) At their highest point, both stones will have the same gravitational potential energy because they reach the same height. D) At its highest point, the heavier stone will have twice as much gravitational potential energy as the lighter one because it is twice as heavy. E) The lighter stone will reach its maximum height sooner than the heavier one.

D

12) 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, and air resistance is negligible. 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? A) Case A B) Case B C) Case C D) Case D E) The speed will be the same in all cases.

E