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John is carrying a shovelful of snow. The center of mass of the 3.00 kg of snow he is holding is 15.0 cm from the end of the shovel. He is pushing down on the opposite end of the shovel with one hand and holding it up 30.0 cm from that end with his other hand. Ignore the mass of the shovel. Sarah says that his hand pushing down on the shovel must be exerting a greater force than the hand pushing up. James says it is just the reverse. Which one, if either, is correct?


A) Sarah, because the hand pushing down must exert a greater force to match the torque exerted by the snow.
B) James, because, depending on the location of the axis of rotation, the hand pushing down can counteract the torque exerted by the snow.
C) James, because the hand pushing up must exert a force that equals the sum of the force of the hand pushing down and the weight of the snow.
D) James, because both (b) and (c) above are correct.
E) Neither, because the hands exert forces of equal magnitudes.

F) A) and E)
G) None of the above

Correct Answer

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C

A square of side A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . - The displacement of the y coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . - The displacement of the y coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . ​ Use this exhibit to answer the following question(s) . - The displacement of the y coordinate of the center of mass (from C to C') is


A) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . - The displacement of the y coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . .
B) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . - The displacement of the y coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . .
C) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . - The displacement of the y coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . .
D) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . - The displacement of the y coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . .
E) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . - The displacement of the y coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . .

F) A) and D)
G) A) and E)

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A

The free-body diagram below represents a 1500-kg car sitting on a 3000-kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below: ​ The free-body diagram below represents a 1500-kg car sitting on a 3000-kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below: ​ ​ ​ A) never produces a torque on the bridge no matter where the axis of rotation is placed. B) never produces a torque on the bridge no matter where the axis of rotation is placed. C) cannot produce a torque on the bridge no matter where the axis of rotation is taken since it is at the center of the bridge. D) Because the perpendicular distance to from the left end of the bridge is 0, F1L should be 0. E) Because the perpendicular distance to from the right end of the bridge is 0, F2L should be 0. ​ The free-body diagram below represents a 1500-kg car sitting on a 3000-kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below: ​ ​ ​ A) never produces a torque on the bridge no matter where the axis of rotation is placed. B) never produces a torque on the bridge no matter where the axis of rotation is placed. C) cannot produce a torque on the bridge no matter where the axis of rotation is taken since it is at the center of the bridge. D) Because the perpendicular distance to from the left end of the bridge is 0, F1L should be 0. E) Because the perpendicular distance to from the right end of the bridge is 0, F2L should be 0. ​


A) The free-body diagram below represents a 1500-kg car sitting on a 3000-kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below: ​ ​ ​ A) never produces a torque on the bridge no matter where the axis of rotation is placed. B) never produces a torque on the bridge no matter where the axis of rotation is placed. C) cannot produce a torque on the bridge no matter where the axis of rotation is taken since it is at the center of the bridge. D) Because the perpendicular distance to from the left end of the bridge is 0, F1L should be 0. E) Because the perpendicular distance to from the right end of the bridge is 0, F2L should be 0. never produces a torque on the bridge no matter where the axis of rotation is placed.
B) The free-body diagram below represents a 1500-kg car sitting on a 3000-kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below: ​ ​ ​ A) never produces a torque on the bridge no matter where the axis of rotation is placed. B) never produces a torque on the bridge no matter where the axis of rotation is placed. C) cannot produce a torque on the bridge no matter where the axis of rotation is taken since it is at the center of the bridge. D) Because the perpendicular distance to from the left end of the bridge is 0, F1L should be 0. E) Because the perpendicular distance to from the right end of the bridge is 0, F2L should be 0. never produces a torque on the bridge no matter where the axis of rotation is placed.
C) The free-body diagram below represents a 1500-kg car sitting on a 3000-kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below: ​ ​ ​ A) never produces a torque on the bridge no matter where the axis of rotation is placed. B) never produces a torque on the bridge no matter where the axis of rotation is placed. C) cannot produce a torque on the bridge no matter where the axis of rotation is taken since it is at the center of the bridge. D) Because the perpendicular distance to from the left end of the bridge is 0, F1L should be 0. E) Because the perpendicular distance to from the right end of the bridge is 0, F2L should be 0. cannot produce a torque on the bridge no matter where the axis of rotation is taken since it is at the center of the bridge.
D) Because the perpendicular distance to The free-body diagram below represents a 1500-kg car sitting on a 3000-kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below: ​ ​ ​ A) never produces a torque on the bridge no matter where the axis of rotation is placed. B) never produces a torque on the bridge no matter where the axis of rotation is placed. C) cannot produce a torque on the bridge no matter where the axis of rotation is taken since it is at the center of the bridge. D) Because the perpendicular distance to from the left end of the bridge is 0, F1L should be 0. E) Because the perpendicular distance to from the right end of the bridge is 0, F2L should be 0. from the left end of the bridge is 0, F1L should be 0.
E) Because the perpendicular distance to The free-body diagram below represents a 1500-kg car sitting on a 3000-kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below: ​ ​ ​ A) never produces a torque on the bridge no matter where the axis of rotation is placed. B) never produces a torque on the bridge no matter where the axis of rotation is placed. C) cannot produce a torque on the bridge no matter where the axis of rotation is taken since it is at the center of the bridge. D) Because the perpendicular distance to from the left end of the bridge is 0, F1L should be 0. E) Because the perpendicular distance to from the right end of the bridge is 0, F2L should be 0. from the right end of the bridge is 0, F2L should be 0.

F) A) and E)
G) A) and D)

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An object of mass m is suspended by two coplanar wires, as shown below. The tension in each wire has a magnitude given by An object of mass m is suspended by two coplanar wires, as shown below. The tension in each wire has a magnitude given by A) . B) . C) . D) mg. E) .


A) An object of mass m is suspended by two coplanar wires, as shown below. The tension in each wire has a magnitude given by A) . B) . C) . D) mg. E) . .
B) An object of mass m is suspended by two coplanar wires, as shown below. The tension in each wire has a magnitude given by A) . B) . C) . D) mg. E) . .
C) An object of mass m is suspended by two coplanar wires, as shown below. The tension in each wire has a magnitude given by A) . B) . C) . D) mg. E) . .
D) mg.
E) An object of mass m is suspended by two coplanar wires, as shown below. The tension in each wire has a magnitude given by A) . B) . C) . D) mg. E) . .

F) A) and B)
G) C) and E)

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A horizontal uniform 1.20-N meter stick is held up by two vertical strings, one at the 20-cm mark and the other at the 60-cm mark. What is the tension in the string at the 60-cm mark?


A) 0.30 N
B) 0.45 N
C) 0.60 N
D) 0.90 N
E) 1.0 N

F) C) and D)
G) A) and D)

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A uniform 100-lb beam is held in a vertical position by a pin at its lower end and a cable at its upper end. A horizontal force (magnitude P) acts as shown in the figure. If P = 75 lb, what is the tension in the cable? A uniform 100-lb beam is held in a vertical position by a pin at its lower end and a cable at its upper end. A horizontal force (magnitude P) acts as shown in the figure. If P = 75 lb, what is the tension in the cable? A) 54 lb B) 69 lb C) 47 lb D) 61 lb E) 75 lb


A) 54 lb
B) 69 lb
C) 47 lb
D) 61 lb
E) 75 lb

F) B) and E)
G) C) and D)

Correct Answer

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A square of side A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The distance from C to C' is A) . B) . C) . D) . E) . is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The distance from C to C' is A) . B) . C) . D) . E) . ​ Use this exhibit to answer the following question(s) . -The distance from C to C' is


A) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The distance from C to C' is A) . B) . C) . D) . E) . .
B) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The distance from C to C' is A) . B) . C) . D) . E) . .
C) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The distance from C to C' is A) . B) . C) . D) . E) . .
D) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The distance from C to C' is A) . B) . C) . D) . E) . .
E) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The distance from C to C' is A) . B) . C) . D) . E) . .

F) A) and D)
G) A) and C)

Correct Answer

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A square of side A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The displacement of the x coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The displacement of the x coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . ​ Use this exhibit to answer the following question(s) . -The displacement of the x coordinate of the center of mass (from C to C') is


A) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The displacement of the x coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . .
B) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The displacement of the x coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . .
C) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The displacement of the x coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . .
D) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The displacement of the x coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . .
E) A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. ​ ​ Use this exhibit to answer the following question(s) . -The displacement of the x coordinate of the center of mass (from C to C') is A) . B) . C) . D) . E) . .

F) A) and E)
G) All of the above

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Stress is proportional to strain means that


A) stress = constant × strain.
B) stress = (constant 1) × strain + constant 2.
C) stress = Stress is proportional to strain means that A) stress = constant × strain. B) stress = (constant 1) × strain + constant 2. C) stress = . D) stress = . E) stress × strain = constant. .
D) stress = Stress is proportional to strain means that A) stress = constant × strain. B) stress = (constant 1) × strain + constant 2. C) stress = . D) stress = . E) stress × strain = constant. .
E) stress × strain = constant.

F) A) and E)
G) B) and D)

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The figure shows a uniform, horizontal beam (length = 10 m, mass = 25 kg) that is pivoted at the wall, with its far end supported by a cable that makes an angle of 51° with the horizontal. If a person (mass = 60 kg) stands 3.0 m from the pivot, what is the tension in the cable? The figure shows a uniform, horizontal beam (length = 10 m, mass = 25 kg) that is pivoted at the wall, with its far end supported by a cable that makes an angle of 51° with the horizontal. If a person (mass = 60 kg) stands 3.0 m from the pivot, what is the tension in the cable? A) 0.83 kN B) 0.30 kN C) 0.38 kN D) 0.42 kN E) 3.0 kN


A) 0.83 kN
B) 0.30 kN
C) 0.38 kN
D) 0.42 kN
E) 3.0 kN

F) B) and D)
G) B) and C)

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The center of gravity of an object is at the same position as the center of mass when


A) The center of gravity of an object is at the same position as the center of mass when A) is the same at both ends of the object. B) the object is located in a region where is uniform over the entire object. C) the object is as large as the body that exerts the gravitational force on it. D) any of the conditions above is satisfied. E) either (a) or (b) above is satisfied. is the same at both ends of the object.
B) the object is located in a region where The center of gravity of an object is at the same position as the center of mass when A) is the same at both ends of the object. B) the object is located in a region where is uniform over the entire object. C) the object is as large as the body that exerts the gravitational force on it. D) any of the conditions above is satisfied. E) either (a) or (b) above is satisfied. is uniform over the entire object.
C) the object is as large as the body that exerts the gravitational force on it.
D) any of the conditions above is satisfied.
E) either (a) or (b) above is satisfied.

F) B) and C)
G) C) and E)

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Find the minimum diameter of a steel wire 18 m long that will stretch no more than 9 mm when a load of 380 kg is hung on the lower end. (Y steel = 2.0 × 1011 N/m2)

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One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium? One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium? A) . B) . C) . D) . E) .


A) One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium? A) . B) . C) . D) . E) . .
B) One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium? A) . B) . C) . D) . E) . .
C) One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium? A) . B) . C) . D) . E) . .
D) One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium? A) . B) . C) . D) . E) . .
E) One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium? A) . B) . C) . D) . E) . .

F) C) and E)
G) C) and D)

Correct Answer

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A 25-ft long crane supported at its lower end by a pin is elevated by a horizontal cable as shown in the figure. A 250-lb load is suspended from the outer end of the crane. The center of gravity of the crane is 10 ft from the pin, and the crane weighs 200 lb. What is the tension in the horizontal cable? A 25-ft long crane supported at its lower end by a pin is elevated by a horizontal cable as shown in the figure. A 250-lb load is suspended from the outer end of the crane. The center of gravity of the crane is 10 ft from the pin, and the crane weighs 200 lb. What is the tension in the horizontal cable? A) 610 lb B) 540 lb C) 640 lb D) 570 lb E) 2 000 lb


A) 610 lb
B) 540 lb
C) 640 lb
D) 570 lb
E) 2 000 lb

F) A) and E)
G) A) and C)

Correct Answer

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The 1560 kg solid steel door to a bank vault is 2.00 m high, 1.00-m wide and 10-cm thick. One hinge is 60.0 cm down from the top on the left-hand side of the door. The other hinge is 30.0 cm up from the bottom. What horizontal force, in what direction, does the door exert on the upper hinge?


A) 6950 N, left
B) 6950 N, right
C) 7640 N, left
D) 7640 N, right
E) 15,300 N, left

F) All of the above
G) B) and C)

Correct Answer

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A 20-m long steel wire (cross-section 1.0 cm2, Young's modulus 2.0 × 1011 N/m2) , is subjected to a load of 25 000 N. How much will the wire stretch under the load?


A) 0.25 cm
B) 2.5 cm
C) 12.5 cm
D) 25 cm
E) 1.25 cm

F) B) and D)
G) B) and C)

Correct Answer

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A uniform beam having a mass of 60 kg and a length of 2.8 m is held in place at its lower end by a pin. Its upper end leans against a vertical frictionless wall as shown in the figure. What is the magnitude of the force the pin exerts on the beam? A uniform beam having a mass of 60 kg and a length of 2.8 m is held in place at its lower end by a pin. Its upper end leans against a vertical frictionless wall as shown in the figure. What is the magnitude of the force the pin exerts on the beam? A) 0.68 kN B) 0.57 kN C) 0.74 kN D) 0.63 kN E) 0.35 kN


A) 0.68 kN
B) 0.57 kN
C) 0.74 kN
D) 0.63 kN
E) 0.35 kN

F) D) and E)
G) C) and E)

Correct Answer

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A

A non-uniform meter stick is found to balance on a knife edge at the 60-cm mark. Where is the center of gravity of the meter stick?


A) at the 40-cm mark
B) at the 45-cm mark
C) at the 50-cm mark
D) at the 55-cm mark
E) at a position not given

F) A) and B)
G) A) and C)

Correct Answer

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A uniform ladder 15 ft long is leaning against a frictionless wall at an angle of 53° above the horizontal. The weight of the ladder is 30 pounds. A 75-lb boy climbs 6.0-ft up the ladder. What is the magnitude of the friction force exerted on the ladder by the floor?


A) 43 lb
B) 34 lb
C) 38 lb
D) 47 lb
E) 24 lb

F) A) and E)
G) B) and C)

Correct Answer

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A horizontal uniform meter stick supported at the 50-cm mark has a mass of 0.50 kg hanging from it at the 20-cm mark and a 0.30-kg mass hanging from it at the 60-cm mark. Determine the position on the meter stick at which one would hang a third mass of 0.60 kg to keep the meter stick balanced.


A) 74 cm
B) 70 cm
C) 65 cm
D) 86 cm
E) 62 cm

F) All of the above
G) A) and B)

Correct Answer

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