**INSTANT DOWNLOAD COMPLETE TEST BANK WITH ANSWERS**

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**Sears and Zemansky’s University Physics with Modern Physics 13th Edition by Hugh D. Young- Roger A. Freedman- A. Lewis Ford – Test Bank**

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**Sample Questions**

*University Physics, 13e*** (Young/Freedman)**

**Chapter 6 Work and Kinetic Energy**

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6.1 Conceptual Questions

1) Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is able to push for 5.0 min longer. Compare the work they do.

- A) Both men do positive work, but Joel does 75% more work than Jerry.
- B) Both men do positive work, but Joel does 50% more work than Jerry.
- C) Both men do positive work, but Jerry does 50% more work than Joel.
- D) Both men do positive work, but Joel does 25% more work than Jerry.
- E) Neither of them does any work.

Answer: E

Var: 1

2) A stock person at the local grocery store has a job consisting of the following five segments:

(1) picking up boxes of tomatoes from the stockroom floor

(2) accelerating to a comfortable speed

(3) carrying the boxes to the tomato display at constant speed

(4) decelerating to a stop

(5) lowering the boxes slowly to the floor.

During which of the five segments of the job does the stock person do positive work on the boxes?

- A) (1) and (5)
- B) (1) only
- C) (1), (2), (4), and (5)
- D) (1) and (2)
- E) (2) and (3)

Answer: D

Var: 1

3) A 3.00-kg ball swings rapidly in a complete vertical circle of radius 2.00 m by a light string that is fixed at one end. The ball moves so fast that the string is always taut and perpendicular to the velocity of the ball. As the ball swings from its lowest point to its highest point

- A) the work done on it by gravity and the work done on it by the tension in the string are both equal to -118 J.
- B) the work done on it by gravity is -118 J and the work done on it by the tension in the string is +118 J.
- C) the work done on it by gravity is +118 J and the work done on it by the tension in the string is -118 J.
- D) the work done on it by gravity is -118 J and the work done on it by the tension in the string is zero.
- E) the work done on it by gravity and the work done on it by the tension in the string are both equal to zero.

Answer: D

Var: 1

4) 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 be

- A) 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: B

Var: 1

5) Which of the graphs in the figure illustrates Hooke’s Law?

- A) Graph a
- B) Graph b
- C) Graph c
- D) graph d

Answer: B

Var: 1

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

- A) Graph a
- B) Graph b
- C) Graph c
- D) Graph d

Answer: D

Var: 1

7) 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 is impossible to know without knowing how long each force acts.

Answer: C

Var: 1

8) If a force always acts perpendicular to an object’s direction of motion, that force cannot change the object’s kinetic energy.

- A) True
- B) False

Answer: A

Var: 1

9) Three cars (car *F*, car *G*, and car *H*) are moving with the same velocity when the driver suddenly slams on the brakes, locking the wheels. The most massive car is car *F*, the least massive is car *H*, and all three cars have identical tires.

(a) Which car travels the longest distance to skid to a stop?

- A) Car
*F* - B) Car
*G* - C) Car
*H* - D) They all travel the same distance in stopping.

(b) For which car does friction do the largest amount of work in stopping the car?

- A) Car
*F* - B) Car
*G* - C) Car
*H* - D) The amount of work done by friction is the same for all cars.

Answer: (a) D (b) A

Var: 1

10) Two objects, one of mass *m* and the other of mass 2*m*, are dropped from the top of a building. When they hit the ground

- A) both of them 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 times the kinetic energy of the lighter one.

Answer: B

Var: 1

6.2 Problems

1) Three forces, *F*1 = 20.0 N, *F*2 = 40.0 N, and *F*3 = 10.0 N act on an object with a mass of 2.00 kg which can move along a frictionless inclined plane as shown in the figure. The questions refer to the instant when the object has moved through a distance of 0.600 m along the surface of the inclined plane in the upward direction. Calculate the amount of work done by

(a) *F*1

(b) *F*2

(c) *F*3.

Answer: (a) 12.0 J (b) 20.8 J (c) 0.00 J

Var: 1

2) You carry a 7.0 kg bag of groceries 1.2 m above the level floor at a constant velocity of 75 cm/s across a room that is 2.3m room. How much work do you do on the bag in the process?

- A) 0.0 J
- B) 82 J
- C) 158 J
- D) 134 J

Answer: A

Var: 50+

3) A student slides her 80.0-kg desk across the level floor of her dormitory room a distance 4.00 m at constant speed. If the coefficient of kinetic friction between the desk and the floor is 0.400, how much work did she do?

- A) 128 J
- B) 3.14 kJ
- C) 26.7 J
- D) 1.26 kJ
- E) 24.0 J

Answer: D

Var: 5

4) Find the net work done by friction on the body of a snake slithering in a complete circle of 3.93 m radius. The coefficient of friction between the ground and the snake is 0.25, and the snake’s weight is 54.0 N.

- A) -330 J
- B) 0 J
- C) -3300 J
- D) -670 J

Answer: A

Var: 50+

5) A crane lifts a 425 kg steel beam vertically a distance of 117 m. How much work does the crane do on the beam if the beam accelerates upward at 1.8 m/s2? Neglect frictional forces.

- A) 5.8
*×*105J - B) 3.4
*×*105 J - C) 4.0
*×*105J - D) 4.9
*×*105 J

Answer: A

Var: 50+

6) An airplane flies 120 km at a constant altitude in a direction 30.0° north of east. A wind is blowing that results in a net horizontal force on the plane due to the air of 2.40 kN in a direction 10.0° south of west. How much work is done on the plane by the air?

- A) -2.71 × 108J
- B) -0.985 × 108J
- C) -221 × 108J
- D) 221 × 108J
- E) 0.821 × 108J

Answer: A

Var: 1

7) A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If 908 J of work are done by the strap while moving the suitcase a horizontal distance of 15 m, what is the tension in the strap?

- A) 75 N
- B) 61 N
- C) 85 N
- D) 92 N

Answer: A

Var: 50+

8) An object is acted upon by a force that represented by the force vs. position graph in the figure. What is the work done as the object moves

(a) from 4 m to 6 m?

(b) from 6 m to 12 m?

Answer: (a) 20 J (b) 30 J

Var: 1

9) In the figure, a constant external force *P* = 160 N is applied to a 20.0-kg box, which is on a rough horizontal surface. While the force pushes the box a distance of 8.00 m, the speed changes from 0.500 m/s to 2.60 m/s. The work done by friction during this process is closest to

- A) -1040 J.
- B) +1110 J.
- C) +1170 J.
- D) +1040 J.
- E) -1170 J.

Answer: A

Var: 1

10) In the figure, a 700-kg crate is on a rough surface inclined at 30°. A constant external force *P* = 5600 N is applied horizontally to the crate. As the force pushes the crate a distance of 3.00 m up the incline, the speed changes from 1.40 m/s to 2.50 m/s. How much work does gravity do on the crate during this process?

- A) -10,300 J
- B) -3400 J
- C) +10,300 J
- D) +3400 J
- E) zero

Answer: A

Var: 1

11) A graph of the force on an object as a function of its position is shown in the figure. Determine the amount of work done by this force on an object that moves from *x* = 1.0 m to *x* = 6.0 m. (Assume an accuracy of 2 significant figures for the numbers on the graph.)

- A) 26 J
- B) 29 J
- C) 22 J
- D) 35 J
- E) 27 J

Answer: A

Var: 5

12) A graph of the force on an object as a function of its position is shown in the figure. Determine the amount of work done by this force on the object during a displacement from *x* = -2.00 m to *x* = 2.00 m. (Assume an accuracy of 3 significant figures for the numbers on the graph.)

- A) -12.0 J
- B) -3.00 J
- C) -1.00 J
- D) 12.0 J
- E) 3.00 J

Answer: C

Var: 1

13) A force = 12 N** î **– 10 N

**acts on an object. How much work does this force do as the object moves from the origin to the point**

*ĵ*- A) 46 J
- B) 266 J
- C) 37 J
- D) 62 J

Answer: A

Var: 8

14) 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 N
- B) 91.0 N
- C) 145 N
- D) 279 N

Answer: A

Var: 50+

15) 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/s^{2}, what is the mass of the object?

- A) 20 kg
- B) 17 kg
- C) 22 kg
- D) 26 kg

Answer: A

Var: 18

16) 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: A

Var: 1

17) 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: B

Var: 1

18) 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: C

Var: 1

19) A force on a particle depends on position such that F(*x*) = (3.00 N/m^{2})*x*^{2} + (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 J
- B) 20.0 J
- C) -48.0 J
- D) 24.0 J
- E) 48.0 J

Answer: B

Var: 5

20) 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 J
- B) 826 J
- C) 495 J
- D) 925 J

Answer: A

Var: 50+

21) 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/m
- B) 44 N/m
- C) 29 N/m
- D) 22 N/m

Answer: A

Var: 50+

22) A force* F = bx*3 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 J
- B) 13 J
- C) 50 J
- D) 57 J

Answer: A

Var: 13

23) 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: A

Var: 1

24) 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/h
- B) 63 km/h
- C) 54 km/h
- D) 36 km/h

Answer: A

Var: 50+

25) 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 MJ
- B) 10.0 kJ
- C) 20.0 kJ
- D) 40.0 kJ
- E) 0.960 MJ

Answer: A

Var: 1

26) 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: A

Var: 31

27) A worker lifts a 20.0-kg bucket of concrete from the ground up to the top of a 20.0-m tall building. The bucket is initially at rest, but is traveling at 4.0 m/s when it reaches the top of the building. What is the minimum amount of work that the worker did in lifting the bucket?

- A) 3.92 kJ
- B) 400 J
- C) 560 J
- D) 4.08 kJ
- E) 160 J

Answer: D

Var: 5

28) A ball is thrown upward at an angle with a speed and direction such that it reaches a maximum height of 16.0 m above the point it was released, with no appreciable air resistance. At its maximum height it has a speed of 18.0 m/s. With what speed was the ball released?

- A) 25.3 m/s
- B) 22.2 m/s
- C) 33.0 m/s
- D) 29.2 m/s
- E) 36.9 m/s

Answer: A

Var: 5

29) A 1000 kg car experiences a net force of 9500 N while decelerating from 30.0 m/s to 23.4 m/s. How far does it travel while slowing down?

- A) 18.5 m
- B) 17.4 m
- C) 20.2 m
- D) 21.9 m

Answer: A

Var: 1

30) A constant horizontal pull acts on a sled on a horizontal frictionless ice pond. The sled starts from rest. When the pull acts over a distance *x*, the sled acquires a speed *v* and a kinetic energy *K*. If the same pull instead acts over twice this distance:

- A) The sled’s speed will be 2
*v*and its kinetic energy will be 2*K*. - B) The sled’s speed will be 2
*v*and its kinetic energy will be*K*. - C) The sled’s speed will be
*v*and its kinetic energy will be 2*K*. - D) The sled’s speed will be
*v*and its kinetic energy will be*K*. - E) The sled’s speed will be 4
*v*and its kinetic energy will be 2

Answer: C

Var: 1

31) In the figure, a 900-kg crate is on a rough surface inclined at 30°. A constant external force *P* = 7200 N is applied horizontally to the crate. While this force pushes the crate a distance of 3.0 m up the incline, its velocity changes from 1.2 m/s to 2.3 m/s. How much work does friction do during this process?

- A) -3700 J
- B) -7200 J
- C) +3700 J
- D) +7200 J
- E) zero

Answer: A

Var: 50+

32) A 5.00-kg box slides 4.00 m across the floor before coming to rest. What is the coefficient of kinetic friction between the floor and the box if the box had an initial speed of 3.00 m/s?

- A) 1.13
- B) 0.587
- C) 0.115
- D) 0.229
- E) 0.267

Answer: C

Var: 5

33) 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 identical conditions?

- A) It would have skidded 4 times farther.
- B) It would have skidded 2 times farther.
- C) It would have skidded times farther.
- D) It would have skidded 1/times farther.
- E) It would have skidded 1/2 as far.

Answer: A

Var: 1

34) In the figure, two boxes, each of mass 24 kg, are at rest and connected as shown. The coefficient of kinetic friction between the inclined surface and the box is 0.31. Find the speed of the boxes just after they have moved 1.6 m.

Answer: 1.9 m/s

Var: 1

35) A 4.00-kg mass is attached to a very light ideal spring hanging vertically and hangs at rest in the equilibrium position. The spring constant of the spring is 1.00 N/cm. The mass is pulled downward 2.00 cm and released. What is the speed of the mass when it is 1.00 cm above the point from which it was released?

- A) 0.0443 m/s
- B) 0.0744 m/s
- C) 0.0201 m/s
- D) 0.0866 m/s
- E) The mass will not reach the height specified.

Answer: D

Var: 5

36) An unusual spring has a restoring force of magnitude *F* = (2.00 N/m)*x* + (1.00 N/m2)*x*2, where *x* is the stretch of the spring from its equilibrium length. A 3.00-kg object is attached to this spring and released from rest after stretching the spring 1.50 m. If the object slides over a frictionless horizontal surface, how fast is it moving when the spring returns to its equilibrium length?

- A) 2.06 m/s
- B) 4.33 m/s
- C) 3.27 m/s
- D) 5.48 m/s
- E) 1.50 m/s

Answer: E

Var: 5

37) The force on a 3.00-kg object as a function of position is shown in the figure. If an object is moving at 2.50 m/s when it is located at *x* = 2.00 m, what will its speed be when it reaches *x* = 8.00 m? (Assume that the numbers on the graph are accurate to 3 significant figures.)

- A) 3.25 m/s
- B) 3.70 m/s
- C) 4.10 m/s
- D) 2.90 m/s
- E) 4.50 m/s

Answer: A

Var: 1

38) A 7.0-kg rock is subject to a variable force given by the equation

* F*(*x*) = 6.0 N – (2.0 N/m)*x* + (6.0 N/m2)*x*2

If the rock initially is at rest at the origin, find its speed when it has moved 9.0 m.

Answer: 20 m/s

Var: 1

39) A 1500-kg car accelerates from 0 to 25 m/s in 7.0 s with negligible friction and air resistance. What is the average power delivered by the engine? (1 hp = 746 W)

- A) 50 hp
- B) 60 hp
- C) 70 hp
- D) 80 hp
- E) 90 hp

Answer: E

Var: 1

40) A child pulls on a wagon with a horizontal force of 75 N. If the wagon moves horizontally a total of 42 m in 3.0 min, what is the average power generated by the child?

- A) 18 W
- B) 22 W
- C) 24 W
- D) 27 W

Answer: A

Var: 29

41) A car needs to generate 75.0 hp in order to maintain a constant velocity of 27.3 m/s on a flat road. What is the magnitude of the total resistive force acting on the car (due to friction, air resistance, etc.)? (1 hp = 746 W)

- A) 2.05
*×*103N - B) 2.75 N
- C) 1.03
*×*103N - D) 2.87
*×*103N

Answer: A

Var: 50+

42) How long will it take a 7.08 hp motor to lift a 250 kg beam directly upward at constant velocity from the ground to a height of 45.0 m? Assume frictional forces are negligible. (1 hp = 746 W)

- A) 20.9 s
- B) 1.56
*×*104s - C) 2.18
*×*104s - D) 39.7 s

Answer: A

Var: 50+

43) Calculate the minimum average power output necessary for a 55.8 kg person to run up a 12.0 m long hillside, which is inclined at 25.0° above the horizontal, in 3.00 s. You can neglect the person’s kinetic energy. Express your answer in horsepower. (1 hp = 746 W)

- A) 1.24 hp
- B) 2.93 hp
- C) 1.86 hp
- D) 0.740 hp

Answer: A

Var: 50+

44) If electricity costs 6.00¢/kWh (kilowatt-hour), how much would it cost you to run a 120 W stereo system 4.0 hours per day for 4.0 weeks?

- A) $0.81
- B) $0.12
- C) $1.38
- D) $2.27

Answer: A

Var: 50+

45) The work performed as a function of time for a process is given by *W* = *at** ^{3}* where

*a*= 2.4 J/s

^{3}. What is the instantaneous power output at

*t*= 3.7 s?

- A) 99 W
- B) 69 W
- C) 138 W
- D) 207 W

Answer: A

Var: 26

*University Physics, 13e*** (Young/Freedman)**

**Chapter 7 Potential Energy and Energy Conservation**

** **

7.1 Conceptual Questions

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.

Answer: C

Var: 1

2) 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 *v*1 of a swimmer reaching the end of slide 1 compares with *v*2, the speed of a swimmer reaching the end of slide 2?

- A)
*v*1>*v*2 - B)
*v*1<*v*2 - C)
*v*1=*v*2 - D) No simple relationship exists between
*v*1and*v*2because we do not know the curvature of slide 2.

Answer: C

Var: 1

3) Two stones, one of mass *m* and the other of mass 2*m*, 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.

Answer: D

Var: 1

4) Two identical balls are thrown directly upward, ball A at speed *v* and ball* B* at speed 2*v*, 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.

Answer: B

Var: 1

5) A box of mass *m* is pressed against (but is not attached to) an ideal spring of force constant *k* and negligible mass, compressing the spring a distance* x*. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment with a box of mass 2*m*

* *

- A) the lighter box will go twice as high up the incline as the heavier box.
- B) just as it moves free of the spring, the lighter box will be moving twice as fast as the heavier box.
- C) both boxes will have the same speed just as they move free of the spring.
- D) both boxes will reach the same maximum height on the incline.
- E) just as it moves free of the spring, the heavier box will have twice as much kinetic energy as the lighter box.

Answer: A

Var: 1

6) A box of mass *m* is pressed against (but is not attached to) an ideal spring of force constant *k* and negligible mass, compressing the spring a distance *x*. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment but instead compress the spring a distance of 2*x*

- A) the box will go up the incline twice as high as before.
- B) just as it moves free of the spring, the box will be traveling twice as fast as before.
- C) just as it moves free of the spring, the box will be traveling four times as fast as before.
- D) just as it moves free of the spring, the box will have twice as much kinetic energy as before.
- E) just before it is released, the box has twice as much elastic potential energy as before.

Answer: B

Var: 1

7) A box of mass *m* is pressed against (but is not attached to) an ideal spring of force constant *k* and negligible mass, compressing the spring a distance *x*. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment but instead use a spring having force constant 2*k*

- A) the box will go up the incline twice as high as before.
- B) just as it moves free of the spring, the kinetic energy of the box will be twice as great as before.
- C) just as it moves free of the spring, the speed of the box will be times as great as before.
- D) All of the above choices are correct.
- E) None of the above choices is correct.

Answer: D

Var: 1

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

Answer: A

Var: 1

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

Answer: A

Var: 1

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

Answer: C

Var: 1

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.

Answer: D

Var: 1

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.

Answer: E

Var: 1

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.

Answer: D

Var: 1

14) A potential energy function for system 1 is given by *U*1(*x*) = *Cx*2 + *Bx*3. The potential energy function for system 2 is given by *U*2(*x*) = *A* + *Cx*2 + *Bx*3, 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.

Answer: B

Var: 1

15) The plot in the figure shows the potential energy of a particle, due to the force exerted on it by another particle, as a function of distance. At which of the three points labeled in the figure is the magnitude of the force on the particle greatest?

- A) point X
- B) point Y
- C) point Z

Answer: A

Var: 1

7.2 Problems

1) An 8.0-kg block is released from rest, with *v*1 = 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 *v*2 = 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

Answer: A

Var: 1

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

Answer: A

Var: 50+

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

Answer: A

Var: 50+

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

Answer: A

Var: 50+

5) It requires 6.0 J of work is needed to push a 2.0-kg object from point *A* to point *B* of the frictionless ramp as shown in the figure. What is the length *s* of the ramp from *A* to *B*?

Answer: 0.61 m

Var: 1

6) A 2.0 g bead slides along a frictionless wire, as shown in the figure. At point *A*, the bead is moving to the right but with negligible speed.

(a) What is the potential energy of the bead at point *A*?

(b) What is the kinetic energy of the bead at point *B*?

(c) What is the speed of the bead at point *B*?

(d) What is the speed of the bead at point *C*?

Answer: (a) 2.0 × 10-2 J (b) 2.0 × 10-2 J (c) 4.4 m/s (d) 2.0 m/s

Var: 1

7) A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position *A* as shown in the figure. The vertical height above ground level at position *A* is 200 m. Neglect friction.

(a) What is the total mechanical energy of the roller coaster at point *A*?

(b) What is the total mechanical energy of the roller coaster at point *B*?

(c) What is the speed of the roller coaster at point *B*?

(d) What is the speed of the roller coaster at point *C*?

Answer: (a) 1.73 × 105 J (b) 1.73 × 105 J (c) 65.7 m/s (d) 34.4 m/s

Var: 1

8) A mass is pressed against (but is not attached to) an ideal horizontal spring on a frictionless horizontal surface. After being released from rest, the mass acquires a maximum speed *v* and a maximum kinetic energy *K*. If instead the mass initially compresses the spring twice as far:

- A) Its maximum speed will be 2
*v*and its maximum kinetic energy will be 2*K*. - B) Its maximum speed will be 2
*v*and its maximum kinetic energy will be*K*. - C) Its maximum speed will be
*v*and its maximum kinetic energy will be 2*K*. - D) Its maximum speed will be 2
*v*and its maximum kinetic energy will be 4*K*. - E) Its maximum speed will be 4
*v*and its maximum kinetic energy will be 2*K*.

Answer: C

Var: 1

9) A 2.0 kg mass is moving along the *x*-axis. The potential energy curve as a function of position is shown in the figure. The kinetic energy of the object at the origin is 12 J. The system is conservative, and there is no friction.

(a) What will be the kinetic energy at 2.0 m along the +*x*-axis?

(b) What will be the speed of the object at 6.0 m along the +*x*-axis?

Answer: (a) 24 J (b) 2.2 m/s

Var: 1

10) An 8.0-m massless rod is loosely pinned to a frictionless pivot at *0*, as shown in the figure. A very small 4.0-kg ball is attached to the other end of the rod. The ball is held at *A*, where the rod makes a 30° angle above the horizontal, and is released. The ball-rod assembly then swings freely with negligible friction in a vertical circle between *A* and *B*. The tension in the rod when the ball passes through the lowest point at *D* is closest to

- A) 160 N.
- B) 200 N.
- C) 120 N.
- D) 80 N.
- E) 40 N.

Answer: A

Var: 1

11) In the figure, a 4.0-kg ball is on the end of a 1.6-m rope that is fixed at *0*. The ball is held at point *A*, with the rope horizontal, and is given an initial downward velocity. The ball moves through three quarters of a circle with no friction and arrives at *B*, with the rope barely under tension. The initial velocity of the ball, at point *A*, is closest to

- A) 4.0 m/s
- B) 5.6 m/s
- C) 6.3 m/s
- D) 6.9 m/s
- E) 7.9 m/s

Answer: D

Var: 1

12) In the figure, a very small toy race car of mass* m* is released from rest on the loop-the-loop track. If it is released at a height 2*R* above the floor, how high is it above the floor when it leaves the track, neglecting friction?

- A) 1.67
*R* - B) 2.00
*R* - C) 1.50
*R* - D) 1.33
*R* - E) 1.25
*R*

Answer: A

Var: 1

13) In the figure, a 5.00-kg block is moving at 5.00 m/s along a horizontal frictionless surface toward an ideal massless 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 it has moved so that the spring is compressed to only one-half of the maximum distance?

Answer: 4.3 m/s

Var: 1

14) A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass. The platform drops 6.00 cm before the person comes to rest. What is the spring constant of the spring?

- A) 2.56 × 105N/m
- B) 3.92 × 105N/m
- C) 5.45 × 104N/m
- D) 4.12 × 105N/m
- E) 8.83 × 104N/m

Answer: D

Var: 1

15) 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 above its point of release. 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 friction and assume the spring is ideal and massless.)

- A) 6.0 m
- B) 12 m
- C) 3.0 m
- D) 48 m

Answer: A

Var: 1

16) A block slides down a frictionless inclined ramp. If the ramp angle is 17.0° and its length is 30.0 m, find the speed of the block as it reaches the bottom of the ramp, assuming it started sliding from rest at the top.

- A) 13.1 m/s
- B) 172 m/s
- C) 9.26 m/s
- D) 24.0 m/s

Answer: A

Var: 50+

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)/*x*2. 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

Answer: D

Var: 1

18) A car on a roller coaster starts at zero speed at an elevation above the ground of 26 m. It coasts down a slope, and then climbs a hill. The top of the hill is at an elevation of 16 m. What is the speed of the car at the top of the hill? Neglect any frictional effects.

- A) 14 m/s
- B) 18 m/s
- C) 10 m/s
- D) 9.0 m/s
- E) 6.0 m/s

Answer: A

Var: 1

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) 4 m/s
- C) 28.7 m/s
- D) 26.7 m/s
- E) 28.1 m/s

Answer: D

Var: 1

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

Answer: D

Var: 1

21) A 2.0-kg object is moving without friction along the *x*-axis. The potential energy curve as a function of position is shown in the figure, and the system is conservative. If the speed of the object at the origin is 4.0 m/s, what will be its speed at 7.0 m along the +*x*-axis?

- A) 4.0 m/s
- B) 4.2 m/s
- C) 4.4 m/s
- D) 4.6 m/s
- E) 9.8 m/s

Answer: B

Var: 1

22) A small hockey puck slides without friction over the icy hill shown in the figure and lands 6.20 m from the foot of the cliff with no air resistance. What was its speed *v*0 at the bottom of the hill?

- A) 20.8 m/s
- B) 17.4 m/s
- C) 14.4 m/s
- D) 13.7 m/s
- E) 4.71 m/s

Answer: D

Var: 1

23) An object is attached to a hanging unstretched ideal and massless spring and slowly lowered to its equilibrium position, a distance of 6.4 cm below the starting point. If instead of having been lowered slowly the object was dropped from rest, how far then would it then stretch the spring at maximum elongation?

- A) 13 cm
- B) 9.1 cm
- C) 6.4 cm
- D) 18 cm
- E) 26 cm

Answer: A

Var: 50+

24) In the figure, a stunt car driver negotiates the frictionless track shown in such a way that the car is barely in contact with the track at the top of the loop. The radius of the track is 9.9 m and the mass of the car is 1800 kg. Find the magnitude of the force of the car on the track when the car is at point *A*. You can treat the car as a point mass.

Answer: 53,000 N

Var: 1

25) A 50.0-kg skier starting from rest travels 200 m down a hill that has a 20.0° slope and a uniform surface. When the skier reaches the bottom of the hill, her speed is 30.0 m/s.

(a) How much work is done by friction as the skier comes down the hill?

(b) What is the magnitude of the friction force if the skier travels directly down the hill?

Answer: (a) -1.10 × 104 J (b) 55.3 N

Var: 1

26) A 5.00-kg object moves clockwise around a 50.0 cm radius circular path. At one location, the speed of the object is 4.00 m/s. When the object next returns to this same location, the speed is 3.00 m/s.

(a) How much work was done by nonconservative (dissipative) forces as the object moved once around the circle?

(b) If the magnitude of the above nonconservative (dissipative) forces acting on the object is constant, what is the value of this magnitude?

Answer: (a) —17.5 J (b) 5.57 N

Var: 1

27) In the figure, a block of mass *m* is moving along the horizontal frictionless surface with a speed of 5.70 m/s. If the slope is 11.0° and the coefficient of kinetic friction between the block and the incline is 0.260, how far does the block travel up the incline?

Answer: 3.72 m

Var: 1

28) An object of mass 4.0 kg starts at rest from the top of a rough inclined plane of height 10 m as shown in the figure. If the speed of the object at the bottom of the inclined plane is 10 m/s, how much work does friction do on this object as it slides down the incline?

Answer: -190 J

Var: 1

29) An 0.80-kg block is held in place against the spring by a 67-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity *v*1 = 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity *v*2 = 1.9 m/s 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 over this section is 0.39. The velocity of the block is *v*3 = 1.4 m/s at *C*. The block moves on to *D*, where it stops. The spring constant of the spring is closest to

- A) 3900 N/m.
- B) 2600 N/m.
- C) 2000 N/m.
- D) 1600 N/m.
- E) 1100 N/m.

Answer: A

Var: 1

30) A 1.37-kg block is held in place against the spring by a 74-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity *v*1 = 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity *v*2 = 1.4 m/s 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 over this section is 0.24. The velocity of the block is *v*3 = 1.4 m/s at *C*. The block moves on to *D*, where it stops. The initial compression of the spring is closest to:

- A) 2.7 cm.
- B) 1.4 cm.
- C) 0.96 cm.
- D) 5.3 cm.
- E) 3.6 cm.

Answer: A

Var: 50+

31) A 1.86-kg block is held in place against the spring by a 81-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity *v*1 = 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity *v*2 = 1.9 m/s 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 over this section is 0.28. The velocity of the block is *v*3 = 1.4 m/s at *C*. The block moves on to *D*, where it stops. The height *h* of the ramp is closest to

- A) 11
- B) 7.3
- C) 15
- D) 17
- E) 18

Answer: A

Var: 50+

32) A 2.5-kg box, sliding on a rough horizontal surface, has a speed of 1.2 m/s when it makes contact with a spring (see the figure). The block comes to a momentary halt when the compression of the spring is 5.0 cm. The work done by the friction, from the instant the block makes contact with the spring until it comes to a momentary halt, is -0.50 J.

(a) What is the spring constant of the spring?

(b) What is the coefficient of kinetic friction between the box and the rough surface?

Answer: (a) 1040 N/m (b) 0.41

Var: 1

33) The only force acting on an object moving along the *x-*axis is the conservative force given by *F*(*x*) = (2.00 N/m)*x* + (1.00 N/m3)*x*3.

(a) What is the change in potential energy when the object moves from *x* = 1.00 m to *x* = 2.00 m?

(b) What is the change in kinetic energy when the object moves from *x* = 1.00 m to *x* = 2.00 m?

Answer: (a) -6.75 J (b) 6.75 J

Var: 1

34) A force on an object is given by *F*(*x*) = (2.00 N/m)*x* – (3.00 N/m3)*x*3. What is a potential energy function *U*(*x*) for this conservative force?

Answer: *U*(*x*)* = *(-1.00 N/m)*x*2 + (0.750 N/m3)*x*4

Var: 1

35) A force on an object is given by *F*(*x*) = ( -4.00 N/m)*x* + ( 2.00 N/m3)*x*3. What is the change in potential energy in moving from *x* = 1.00 m to *x* = 2.00 m?

- A) 10.0 J
- B) -1.50 J
- C) -10.0 J
- D) 1.50 J
- E) 12.0 J

Answer: B

Var: 1

36) A potential energy function is given by *U*(*x*) = (3.00 J)*x* + (1.00 J/m2)*x*3. What is the force function *F*(*x*) that is associated with this potential energy function?

Answer: *F*(*x*) = -3.00 N – (3.00 N/m2)*x*2

Var: 1

37) A potential energy function is given by *U*(*x*) = ( 3.00 N/m)*x* – ( 1.00 N/m3)*x*3. At what position or positions is the force equal to zero?

- A) m and -m
- B) 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.

Answer: C

Var: 1

38) The potential energy for a certain mass moving in one dimension is given by *U*(*x*) = (2.0 J/m3)*x*3 – (15 J/m2)*x*2 + (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

Answer: C

Var: 1

39) A particle experiences a force given by F(x) = *α* – *βx*3. Find the potential field *U*(*x*) the particle is in. (Assume that the zero of potential energy is located at *x* = 0.)

- A)
*U*(*x*) = –*αx*+*x*4 - B)
*U*(*x*) =*αx*–*x*4 - C)
*U*(*x*) = 3*βx*2 - D)
*U*(*x*) = -3*βx*2

Answer: A

Var: 1

40) When a particle is a distance *r* from the origin, its potential energy function is given by the equation *U*(*r*) = *kr*, where *k* is a constant and r =

(a) What are the SI units of *k*?

(b) Find a mathematical expression in terms of *x*, *y*, and *z* for the *y* component of the force on the particle.

(c) If *U* = 3.00 J when the particle is 2.00 m from the origin, find the numerical value of the *y* component of the force on this particle when it is at the point (-1.00 m, 2.00 m, 3.00 m).

Answer: (a) kg ∙ m/s2 (or J/m or N) (b) *Fy* = – (c) -0.802 N

Var: 1

*University Physics, 13e*** (Young/Freedman)**

**Chapter 9 Rotation of Rigid Bodies**

** **

9.1 Conceptual Questions

1) When a rigid body rotates about a fixed axis, all the points in the body have the same

- A) tangential speed.
- B) angular acceleration.
- C) tangential acceleration.
- D) linear displacement.
- E) centripetal acceleration.

Answer: B

Var: 1

2) A horizontal disk rotates about a vertical axis through its center. Point* P* is midway between the center and the rim of the disk, and point *Q* is on the rim. If the disk turns with constant angular velocity, which of the following statements about it are true? (There may be more than one correct choice.)

- A)
*P*and*Q*have the same linear acceleration. - B)
*Q*is moving twice as fast as*P*. - C) The linear acceleration of
*Q*is twice as great as the linear acceleration of*P*. - D) The linear acceleration of
*P*is twice as great as the linear acceleration of*Q*. - E) The angular velocity of
*Q*is twice as great as the angular velocity of*P*.

Answer: B, C

Var: 1

3) As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?

- A) up
- B) down
- C) to your left
- D) to your right
- E) forwards

Answer: B

Var: 1

4) When you ride a bicycle, in what direction is the angular velocity of the wheels?

- A) to your left
- B) to your right
- C) forwards
- D) backwards
- E) up

Answer: A

Var: 1

5) A dumbbell-shaped object is composed by two equal masses, *m*, connected by a rod of negligible mass and length *r. *If *I*1* *is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and *I*2 is the moment of inertia with respect to an axis passing through one of the masses, it follows that

- A)
*I*1=*I*2. - B)
*I*1>*I*2. - C)
*I*2>*I*1.

Answer: C

Var: 1

9.2 Problems

1) A turbine blade rotates with angular velocity ω(*t*) = 2.00 rad/s- 2.1.00 rad/s3 *t*^{2}. What is the angular acceleration of the blade at *t* = 9.1 s?

- A) -38.2 rad/s
^{2} - B) -19.1 rad/s
^{2} - C) -86.0 rad/s
^{2} - D) -36.2 rad/s
^{2} - E) -172 rad/s
^{2}

Answer: A

Var: 50+

2) The angular velocity of a 755-g wheel 15.0 cm in diameter is given by the equation *ω*(*t*) = (2.00 rad/s2)*t* + (1.00 rad/s4)*t*3.

(a) Through how many radians does the wheel turn during the first 2.00 s of its motion?

(b) What is the angular acceleration (in rad/s2) of the wheel at the end of the first 2.00 s of its motion?

Answer: (a) 8.00 rad (b) 14.0 rad/s2

Var: 1

3) The angular acceleration of a wheel is given in rad/s^{2} by 45t^{3} – 11t^{4} where t is in seconds. If the wheel starts from rest at t = 0.00 s, when is the next time the wheel is at rest?

- A) 5.1 s
- B) 8.4 s
- C) 6.9 s
- D) 3.6 s

Answer: A

Var: 36

4) A 1.15-kg grinding wheel 22.0 cm in diameter is spinning counterclockwise at a rate of 20.0 revolutions per second. When the power to the grinder is turned off, the grinding wheel slows with constant angular acceleration and takes 80.0 s to come to a rest.

(a) What was the angular acceleration (in rad/s2) of the grinding wheel as it came to rest if we take a counterclockwise rotation as positive?

(b) How many revolutions did the wheel make during the time it was coming to rest?

Answer: (a) -1.57 rad/s2 (b) 800 revolutions

Var: 1

5) A 3.45-kg centrifuge takes 100 s to spin up from rest to its final angular speed with constant angular acceleration. A point located 8.00 cm from the axis of rotation of the centrifuge moves with a speed of 150 m/s when the centrifuge is at full speed.

(a) What is the angular acceleration (in rad/s2) of the centrifuge as it spins up?

(b) How many revolutions does the centrifuge make as it goes from rest to its final angular speed?

Answer: (a) 18.8 rad/s2 (b) 1.49 × 104 revolutions

Var: 1

6) When a 2.75-kg fan, having blades 18.5 cm long, is turned off, its angular speed decreases uniformly from 10.0 rad/s to 6.30 rad/s in 5.00 s.

(a) What is the magnitude of the angular acceleration of the fan?

(b) Through what angle (in degrees) does it turn while it is slowing down during the 5.00 s?

(c) If its angular acceleration does not change, how long after it is turned off does it take the fan to stop.

Answer: (a) 0.740 rad/s2 (b) 2330° (c) 13.5 s

Var: 1

7) A 4.50-kg wheel that is 34.5 cm in diameter rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel?

- A) 0.616 rad/s2
- B) 5.45 rad/s2
- C) 111 rad/s2
- D) 22.5 rad/s2
- E) 10.9 rad/s2

Answer: E

Var: 1

8) A machinist turns the power on to a grinding wheel, which is at rest at time* t *= 0.00 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 25 rad/s. The wheel is run at that angular velocity for 37 s and then power is shut off. The wheel decelerates uniformly at 1.5 rad/s2 until the wheel stops. In this situation, the time interval of angular deceleration (slowing down) is closest to:

- A) 17 s
- B) 15 s
- C) 19 s
- D) 21 s
- E) 23 s

Answer: A

Var: 50+

9) In the figure, point *P* is at rest when it is on the *x-*axis. The linear speed of point* P* when it reaches the *y*-axis is closest to

- A) 0.18 m/s.
- B) 0.24 m/s.
- C) 0.35 m/s.
- D) 0.49 m/s.
- E) 0.71 m/s.

Answer: C

Var: 1

10) In the figure, point *P* is at rest when it is on the *x-*axis. The time *t*, when *P* returns to the original position on the* x*-axis, is closest to

- A) 13 s.
- B) 18 s.
- C) 25 s.
- D) 35 s.
- E) 50 s.

Answer: D

Var: 1

11) A 1.25-kg ball begins rolling from rest with constant angular acceleration down a hill. If it takes 3.60 s for it to make the first complete revolution, how long will it take to make the next complete revolution?

Answer: 1.49 s

Var: 1

12) A piece of thin uniform wire of mass *m* and length 3*b* is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices.

- A)
*mb*2 - B)
*mb*2 - C)
*mb*2 - D)
*mb*2 - E)
*mb*2

Answer: E

Var: 1

13) A slender uniform rod 100.00 cm long is used as a meter stick. Two parallel axes that are perpendicular to the rod are considered. The first axis passes through the 50-cm mark and the second axis passes through the 30-cm mark. What is the ratio of the moment of inertia through the second axis to the moment of inertia through the first axis?

- A)
*I*2/*I*1= 1.5 - B)
*I*2/*I*1= 1.7 - C)
*I*2/*I*1= 1.9 - D)
*I*2/*I*1= 2.1 - E)
*I*2/*I*1= 2.3

Answer: A

Var: 1

14) A uniform solid sphere has a moment of inertia *I* about an axis tangent to its surface. What is the moment of inertia of this sphere about an axis through its center?

- A) 1/7
*I* - B) 2/7
*I* - C) 2/5
*I* - D) 3/5
*I* - E) 7/5
*I*

Answer: B

Var: 1

15) In the figure, a weightlifter’s barbell consists of two identical uniform spherical masses each with radius 0.17 m and mass of 50 kg. The weights are connected by a 0.96-m uniform steel rod with a mass of 12 kg. Find the moment of inertia of the barbell about the axis through the center (see figure).

Answer: 44 kg∙m2

Var: 1

16) An extremely light rod 1.00 m long has a 2.00-kg mass attached to one end and a 3.00-kg mass attached to the other. The system rotates at a constant angular speed about a fixed axis perpendicular to the rod that passes through the rod 30.0 cm from the end with the 3.00-kg mass attached. The kinetic energy of the system is measured to be 100.0 J.

(a) What is the moment of inertia of this system about the fixed axis?

(b) What is the angular speed (in revolutions per second) of this system?

Answer: (a) 1.25 kg∙m2 (b) 2.01 rev/s

Var: 1

17) A uniform solid sphere of mass *M* and radius *R* rotates with an angular speed *ω* about an axis through its center. A uniform solid cylinder of mass *M*, radius *R*, and length 2*R* rotates through an axis running through the central axis of the cylinder. What must be the angular speed of the cylinder so it will have the same rotational kinetic energy as the sphere?

- A) 2
*ω*/5 - B)
*ω* - C) 4
*ω*/5 - D) 2
*ω*/ - E)
*ω*/

Answer: D

Var: 1

18) While spinning down from 500.0 rpm to rest, a solid uniform flywheel does 5.1 kJ of work. If the radius of the disk is 1.2 m, what is its mass?

- A) 5.2 kg
- B) 4.4 kg
- C) 6.0 kg
- D) 6.8 kg

Answer: A

Var: 50+

19) At any angular speed, a certain uniform solid sphere of diameter *D *has half as much rotational kinetic energy as a certain uniform thin-walled hollow sphere of the same diameter when both are spinning about an axis through their centers. If the mass of the solid sphere is *M*, the mass of the hollow sphere is

- A) 3/5
- B) 5/3
- C) 5/6
- D) 6/5
- E) 2

Answer: D

Var: 1

20) A futuristic design for a car is to have a large solid disk-shaped flywheel within the car storing kinetic energy. The uniform flywheel has mass 370 kg with a radius of 0.500 m and can rotate up to 230 rev/s. Assuming all of this stored kinetic energy could be transferred to the linear velocity of the 1600-kg car, find the maximum attainable speed of the car.

Answer: 246 m/s

Var: 50+

21) In the figure, two blocks, of masses 2.00 kg and 3.00 kg, are connected by a light string that passes over a frictionless pulley of moment of inertia 0.00400 kg · m2 and radius 5.00 cm. The coefficient of friction for the tabletop is 0.300. The blocks are released from rest. Using energy methods, find the speed of the upper block just as it has moved 0.600 m.

- A) 1.22 m/s
- B) 5.44 m/s
- C) 3.19 m/s
- D) 1.95 m/s
- E) 1.40 m/s

Answer: E

Var: 1

*University Physics, 13e*** (Young/Freedman)**

**Chapter 11 Equilibrium and Elasticity**

** **

11.1 Conceptual Questions

1) If the torque on an object adds up to zero

- A) the forces on it also add up to zero.
- B) the object is at rest.
- C) the object cannot be turning.
- D) the object could be accelerating linearly but it could not be turning.
- E) the object could be both turning and accelerating linearly.

Answer: E

Var: 1

2) A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw? Assume that both people are small enough compared to the length of the seesaw to be thought of as point masses.

- A) It is impossible to say without knowing the masses.
- B) It is impossible to say without knowing the distances.
- C) The side the boy is sitting on will tilt downward.
- D) Nothing will happen; the seesaw will still be balanced.
- E) The side the girl is sitting on will tilt downward.

Answer: D

Var: 1

3) Tensile stress is

- A) the strain per unit length.
- B) the same as force.
- C) the ratio of the change in length to the original length.
- D) the applied force per cross-sectional area.
- E) the ratio of elastic modulus to strain.

Answer: D

Var: 1

4) Tensile train is

- A) the ratio of the change in length to the original length.
- B) the stress per unit area.
- C) the same as force.
- D) the applied force per cross-sectional area.
- E) the ratio of stress to elastic modulus.

Answer: A

Var: 1

5) Two compressible solids are formed into spheres of the same size. The bulk modulus of sphere two is twice as large as the bulk modulus of sphere one. You now increase the pressure on both spheres by the same amount. As a result of the increased pressure, how is the change in volume of sphere two (△*V*2) related to the change in volume of sphere one (Δ*V*1)?

- A) Δ
*V*2 = 2Δ*V*1 - B) Δ
*V*2 = 4Δ*V*1 - C) v
*V*2 = Δ*V*1 - D) Δ
*V*2 = 1/2Δ*V*1 - E) Δ
*V*2 = 1/4Δ*V*1

Answer: D

Var: 1

6) Which one of the following stresses would be most likely to cause a bone to fracture?

- A) tensile stress
- B) compressive stress
- C) sheer stress
- D) bulk stress

Answer: C

Var: 1

7) The graph in the figure shows the force on an object as a function of the elongation caused by that force. Which statement about this object is true?

- A) The object obeys Hooke’s law at all points from
*A*to*C*. - B) The object obeys Hooke’s law at all points from
*B*to*C*. - C) The object obeys Hooke’s law at all points from
*A*to*B*. - D) The elastic limit occurs at point
*C*. - E) The region of elastic behavior occurs from
*B*to*C*.

Answer: C

Var: 1

11.2 Problems

1) A light board, 10 m long, is supported by two sawhorses, one at one edge of the board and a second at the midpoint. A small 40-N weight is placed between the two sawhorses, 3.0 m from the edge and 2.0 m from the center. What forces are exerted by the sawhorses on the board?

Answer: 16 N at the end and 24 N at the midpoint

Var: 1

2) An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two narrow pillars 1.60 m apart, as shown in the figure. Find the magnitude and direction of the force exerted on the diving board

(a) by pillar *A*.

(b) by pillar *B*.

Answer: (a) 1.71 kN downwards (b) 2.51 kN upwards

Var: 1

3) A 20.0-kg uniform plank is supported by the floor at one end and by a vertical rope at the other as shown in the figure. A 50.0-kg mass person stands on the plank a distance three-fourths of the length plank from the end on the floor.

(a) What is the tension in the rope?

(b) What is the magnitude of the force that the floor exerts on the plank?

Answer: (a) 466 N (b) 220 N

Var: 1

4) A 3.00-kg ball rests in a frictionless groove as shown in the figure.

(a) What is the magnitude of the force that the left side of the groove exerts on the ball?

(b) What is the magnitude of the force that the right side of the groove exerts on the ball?

Answer: (a) 26.4 N (b) 21.5 N

Var: 1

5) A nonuniform, 80.0-g, meterstick balances when the support is placed at the 51.0-cm mark. At what location on the meterstick should a 5.00-g tack be placed so that the stick will balance at the 50.0 cm mark?

- A) 16.0 cm
- B) 67.0 cm
- C) 66.0 cm
- D) 35.0 cm
- E) 34.0 cm

Answer: E

Var: 1

6) A 30.0-kg child sits on one end of a long uniform beam having a mass of 20.0 kg, and a 40.0-kg child sits on the other end. The beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child. How long is the beam?

- A) 2.12 m
- B) 1.98 m
- C) 1.93 m
- D) 2.07 m
- E) 2.20 m

Answer: B

Var: 1

7) In the figure, the horizontal lower arm has a mass of 2.8 kg and its center of gravity is 12 cm from the elbow joint pivot. How much force *F*M must the vertical extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put?

- A) 100 N
- B) 500 N
- C) 750 N
- D) 1000 N
- E) 1500 N

Answer: D

Var: 1

8) A 5.0-m long, 12-kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 m from the wall. The coefficient of static friction between the floor and the ladder is 0.28. What distance, measured along the ladder from the bottom, can a 60-kg person climb before the ladder starts to slip?

- A) 4.0 m
- B) 3.7 m
- C) 1.7 m
- D) 1.3 m
- E) 3.3 m

Answer: C

Var: 1

9) A stepladder consists of two halves, hinged at the top, and connected by a tie rod that keeps the two halves from spreading apart. In this particular instance, the two halves are 2.50 m long, the tie rod is connected to the center of each half and is 70.0 cm long. An 800-N person stands 3/5 of the way up the stepladder, as shown in the figure. Neglecting the weight of the ladder, and assuming that the ladder is resting on a smooth floor, what is the tension in the tie rod? ** Note:** To solve this problem you must “cut” the ladder in half and consider the equilibrium of forces and torques acting on each half of the ladder.

- A) 140 N
- B) 240 N
- C) 280 N
- D) 360 N
- E) 560 N

Answer: A

Var: 1

10) Two identical ladders are 3.0 m long and weigh 600 N each. They are connected by a hinge at the top and are held together by a horizontal rope, 1.0 m above the smooth floor forming a symmetric “A” arrangement. The angle between the ladders is 60° and both ladders have their center of gravity at their midpoint. What is the tension in the rope?

- A) 240 N
- B) 300 N
- C) 220 N
- D) 260 N
- E) 280 N

Answer: E

Var: 1

11) A 120-kg refrigerator, 2.00 m tall and 85.0 cm wide, has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.300. Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it won’t tip before it begins to slide?

- A) 0.710 m
- B) 1.00 m
- C) 1.21 m
- D) 1.42 m
- E) 1.63 m

Answer: D

Var: 1

12) A child is trying to stack two uniform wooden blocks, 12 cm in length, so they will protrude as much as possible over the edge of a table, without tipping over, as shown in the figure. What is the maximum possible overhang distance *d*?

- A) 5 cm
- B) 6 cm
- C) 7 cm
- D) 8 cm
- E) 9 cm

Answer: E

Var: 1

13) A uniform sign is supported against a wall at point *P* as shown in the figure. If the sign is a square 0.40 m on a side and its mass is 4.0 kg, what is the magnitude of the horizontal force that the wall at *P* experiences?

- A) 20 N
- B) 0.00 N
- C) 7.8 N
- D) 98 N

Answer: A

Var: 50+

14) A uniform 300-kg beam, 6.00 m long, is freely pivoted at *P*, as shown in the figure. The beam is supported in a horizontal position by a light strut, 5.00 m long, which is freely pivoted at *Q* and is loosely pinned to the beam at *R*. A load of mass is suspended from the end of the beam at *S*. A maximum compression of 23,000 N in the strut is permitted, due to safety. The maximum mass *M* of the load is closest to

- A) 789 kg.
- B) 554 kg.
- C) 1020 kg.
- D) 1090 kg.
- E) 1320 kg.

Answer: A

Var: 1

15) A uniform 300-kg beam, 6.00 m long, is freely pivoted at *P*, as shown in the figure. The beam is supported in a horizontal position by a light strut, 5.00 m long, which is freely pivoted at *Q* and is loosely pinned to the beam at *R*. A load of mass is suspended from the end of the beam at *S*. A maximum compression of 23,000 N in the strut is permitted, due to safety. Under maximum load, find the magnitude of the *x* component of the force exerted on the beam by the pivot at *P*.

- A) 13,800 N
- B) 12,800 N
- C) 11,200 N
- D) 14,400 N
- E) 16,000 N

Answer: A

Var: 1

16) A 10.0-kg uniform ladder that is 2.50 m long is placed against a smooth vertical wall and reaches to a height of 2.10 m, as shown in the figure. The base of the ladder rests on a rough horizontal floor whose coefficient of static friction with the ladder is 0.800. An 80.0-kg bucket of concrete is suspended from the top rung of the ladder, right next to the wall, as shown in the figure. What is the magnitude of the friction force that the floor exerts on the ladder?

- A) 538 N
- B) 706 N
- C) 1290 N
- D) 833 N
- E) 601 N

Answer: A

Var: 1

17) A dump truck has a large cubical concrete block in its bed. The coefficients of friction between this block and the floor of the bed are *µ*k = 0.450 and *µ*s = 0.650. As the bed is slowly tilted above the horizontal, will the brick first begin to slide or will it first tip over?

- A) It will first tip over.
- B) It will first begin to slide.
- C) It will tip over just as it begins to slide.
- D) It is impossible to answer without knowing the mass of the block.
- E) It is impossible to answer without knowing the dimensions of the block.

Answer: B

Var: 1

18) A solid uniform brick is placed on a sheet of wood. When one end of the sheet is raised (see figure), you observe that the maximum that the angle *θ* can be without tipping over the brick is 49.6°. There is enough friction to prevent the brick from sliding. What is the width *w* of the brick?

- A) 5.18 cm
- B) 6.09 cm
- C) 6.81 cm
- D) 9.40 cm
- E) 10.5 cm

Answer: D

Var: 1

19) A 20.0-kg uniform door has a width of 1.20 m and a height of 2.50 m. The door is mounted on a post by a pair of hinges, marked 1 and 2 in the figure, at the top and bottom of the door. An external force of 60.0 N, at an angle of 30.0° above the horizontal, is applied to the small doorknob, as shown in the figure. The doorknob is 1.00 m above the bottom of the door.

(a) Find the *x* component of the force that hinge 1 exerts on the door at the top.

(b) Find the SUM of the *y* components of the forces that hinges 1 and 2 together exert on the door.

Answer: (a) -53.4 N (b) 166 N

Var: 1

20) In the figure, a uniform rectangular crate 0.40 m wide and 1.0 m tall rests on a horizontal surface. The crate weighs 930 N, and its center of gravity is at its geometric center. A horizontal force *F* is applied at a distance *h* above the floor. If *h* = 0.61 m, what minimum value of *F* is required to make the crate start to tip over? Static friction is large enough that the crate does not start to slide.

Answer: 305 N

Var: 50+

21) In the figure, a 10.0-m long bar is attached by a frictionless hinge to a wall and held horizontal by a rope that makes an angle *θ* of 53° with the bar. The bar is uniform and weighs 39.9 N. How far from the hinge should a 10.0-kg mass be suspended for the tension *T* in the rope to be 125 N?

Answer: 8.15 m from the hinge

Var: 1

22) In the figure, a uniform ladder 12 meters long rests against a vertical frictionless wall. The ladder weighs 400 N and makes an angle *θ* of 79° with the floor. A man weighing 790 N climbs slowly up the ladder. When he has climbed to a point that is 7.8 m from the base of the ladder, the ladder starts to slip. What is the coefficient of static friction between the floor and the ladder?

Answer: 0.12

Var: 50+

23) A steel guitar string with a diameter of 0.300 mm and a length of 70.0 cm is stretched by 0.500 mm while being tuned. How much force is needed to stretch the string by this amount? Young’s modulus for steel is 2.0 × 1011 N/m2.

Answer: 10.1 N

Var: 1

24) A 1000-kg object hangs from the lower end of a steel rod 5.0 m long that is suspended vertically. The diameter of the rod is 0.80 cm and Young’s modulus for the rod is 210,000 MN/m2. What is the elongation of the rod due to this object?

- A) 1.2 cm
- B) 0.46 cm
- C) 0.12 cm
- D) 1.8 cm
- E) 0.047 cm

Answer: B

Var: 1

25) A 0.600-mm diameter wire stretches 0.500% of its length when it is stretched with a tension of 20.0 N. What is the Young’s modulus of this wire?

- A) 5.66 × 1010N/m2
- B) 3.54 × 109N/m2
- C) 1.41 × 1010N/m2
- D) 6.43 × 109N/m2
- E) 2.78 × 109N/m2

Answer: C

Var: 1

26) A cable is 100 m long, has a cross-sectional area of 1.0 mm2, and is made of a material having a Young’s modulus of 1.0 × 1011 N/m2. If a 1000-N force is applied to stretch the cable, how far does it stretch?

- A) 0.0010 m
- B) 0.010 m
- C) 0.10 m
- D) 1.0 m
- E) 10 m

Answer: D

Var: 1

27) A steel lift column in a service station is a solid cylinder 4.0 m long and 0.20 m in diameter. Young’s modulus for this steel is 20 × 1010 N/m2. By what distance does the column compress when a 5000-kg truck is on it?

- A) 4.7 × 10-7m
- B) 8.0 × 10-7m
- C) 3.2 × 10-6m
- D) 7.8 × 10-6m
- E) 3.1 × 10-5m

Answer: E

Var: 1

28) The tensile strength (the maximum tensile stress it can support without breaking) for a certain steel wire is 3000 MN/m2. What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this steel without breaking the wire?

- A) 64 kN
- B) 9.0 kN
- C) 42 kN
- D) 85 kN
- E) 21 kN

Answer: E

Var: 1

29) A steel rod 55 cm long has a diameter of 30 cm. The compressive strength (the maximum stress it can support without breaking) of this steel is 500 × 106 N/m2. What is the compression force that would break the rod?

- A) 3.5 × 107N
- B) 2.4 × 107N
- C) 1.4 × 108N
- D) 4.7 × 108N
- E) 8.9 × 108N

Answer: A

Var: 1

30) A very light 1.00-m wire consists of two segments of equal length, one of steel (Young’s modulus is 2.00 × 1011 N/m2) and one of brass (Young’s modulus is 9.0 × 1010 N/m2). The steel segment is 1.50 mm in diameter, and the brass segment has twice this diameter. When a weight *w* is hung from the ceiling by this wire, the steel segment stretches by 1.10 mm. Find the weight *w*.

- A) 190 N
- B) 390 N
- C) 780 N
- D) 1000 N
- E) 3100 N

Answer: C

Var: 1

31) A very light 1.00-m wire consists of two segments of equal length, one of steel (Young’s modulus is 2.00 × 1011 N/m2) and one of brass (Young’s modulus is 9.0 × 1010 N/m2). The steel segment is 1.50 mm in diameter, and the brass segment has twice this diameter. When a weight *w* is hung from the ceiling by this wire, the steel segment stretches by 1.10 mm. By what distance does the brass segment stretch?

- A) 0.50 mm
- B) 0.61 mm
- C) 1.2 mm
- D) 2.4 mm
- E) 9.8 mm

Answer: B

Var: 1

32) What is the maximum length of a metal cable that can hang vertically supported from one end of the cable? The Young’s modulus of this metal is 2.10 × 1011 N/m2, its tensile strength (the maximum tensile stress it can support without breaking) is 7.40 × 108 N/m2, and its density is 7.60 × 103 kg/m3.

- A) 9.94 km
- B) 4.22 km
- C) 456 km
- D) 1.75 km
- E) 24.8 km

Answer: A

Var: 1

33) An aluminum wire and a steel wire, each of length 2.0 m, are hung from the ceiling. A 5.0-kg mass is suspended from the lower end of each wire. The aluminum wire has a diameter of 2.2 mm. What must be the diameter of the steel wire if it is to stretch the same distance as the aluminum wire, so that the two wires maintain equal lengths after the masses are attached? Young’s modulus for aluminum is 0.70 × 1011 N/m2 and for steel it is 2.0 × 1011 N/m2.

Answer: 1.3 mm

Var: 1

34) A copper sphere has a radius of 2.50 m under normal room pressure of 1.0 × 105 N/m2. If we increase the pressure on this sphere to 10 times the normal room pressure, what is the change in its volume? The bulk modulus for copper is 1.4 × 1011 Pa.

Answer: -4.2 × 10-4 m3

Var: 1

35) A solid steel sphere with a radius of 2.0 m falls off a ship and sinks to a depth where the pressure is 15 MN/m2. The bulk modulus for this steel is 1.6 × 1011 N/m2. What is the change in the radius of the sphere?

- A) -0.021 mm
- B) -4.2 mm
- C) -0.42 mm
- D) -0.19 mm
- E) -0.062 mm

Answer: E

Var: 1

36) At a depth of about 1030 m in the sea, the pressure has increased by 100 atmospheres (to 1.0 × 107 N/m2). By how much has 1.0 m3 of water been compressed by this pressure? The bulk modulus of water is 2.3 × 109 N/m2.

- A) 2.3 × 10-3m3
- B) 3.3 × 10-3m3
- C) 4.3 × 10-3m3
- D) 5.3 × 10-3m3
- E) 6.3 × 10-3m3

Answer: C

Var: 1

37) A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10-4. The bulk modulus of the oil is 6.0 × 109 N/m2 and is independent of the pressure. By how many milliliters does this pressure reduce the volume of the oil?

- A) 2.0 mL
- B) 2.4 mL
- C) 2.8 mL
- D) 3.2 mL
- E) 3.6 mL

Answer: E

Var: 1

38) A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10-4. The bulk modulus of the oil is 6.0 × 109 N/m2 and is independent of the pressure. What is the pressure change that produced the volume strain in the oil?

- A) 1.2 MN/m2
- B) 1.4 MN/m2
- C) 1.6 MN/m2
- D) 1.8 MN/m2
- E) 2.0 MN/m2

Answer: D

Var: 1

39) When the pressure applied to an unknown liquid is increased from 1.0 × 107 N/m2 to 5.5 × 107 N/m2, the volume of the liquid decreases by 0.70%. Calculate the bulk modulus of the liquid.

Answer: 6.4 × 109 N/m2

Var: 1

40) A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm while the opposite face is held fixed in place. What is the resulting displacement of the face? (The shear modulus for aluminum is 2.5 × 1010 N/m2)

- A) 1.9 × 10-8m
- B) 2.6 × 10-8m
- C) 4.4 × 10-8m
- D) 5.3 × 10-8m
- E) 8.2 × 10-8m

Answer: D

Var: 1

41) The base of an aluminum block, which is fixed in place, measures 90 cm by 90 cm, and the height of the block is 60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of 0.0060. The shear modulus of aluminum is 3.0 × 1010 N/m2. What is the displacement of the upper face in the direction of the applied force?

- A) 3.0 mm
- B) 3.6 mm
- C) 4.2 mm
- D) 4.8 mm
- E) 5.4 mm

Answer: B

Var: 1

42) The base of an aluminum block, which is fixed in place, measures 90 cm by 90 cm, and the height of the block is 60 cm. A force, applied to the upper face and parallel to it, produces a shear strain of 0.0060. The shear modulus of aluminum is 3.0 × 1010 Pa. What is the sheer stress on the block?

- A) 180 × 106N/m2
- B) 360 × 106N/m2
- C) 600 × 106N/m2
- D) 720 × 106N/m2
- E) 900 × 106N/m2

Answer: A

Var: 1

43) A sample of tendon 3.00 cm long and 4.00 mm in diameter is found to break under a minimum force of 128 N. If instead the sample had been 1.50 cm long and of uniform composition and cross-sectional area, what minimum force would have been required to break it?

- A) 32 N
- B) 64 N
- C) 128 N
- D) 256 N
- E) 512 N

Answer: C

Var: 1