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Exam 8: Equilibrium Ad Elasticity

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Question 31

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Tensile stress is

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

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

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Question 32

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A very light ideal spring stretches by $21.0 \mathrm {~cm}$ when it is used to hang a 135-N object. What is the weight of a piece of electronic equipment that would stretch the spring by $44.9 \mathrm {~cm}$ if you hung the equipment using the spring?

A) 289 N
B) 63 N
C) 176 N
D) 405 N

E) B) and C)
F) A) and D)

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Question 33

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An 82-kg diver stands at the edge of a light 5.0-m diving board, which is supported by two vertical pillars that are 1.6 m apart, as shown in the figure. Find the magnitude and direction of the force exerted by each pillar.

In the figure, a uniform ladder of weight 200 N and length 10 m leans against a perfectly smooth wall. A firefighter of weight 600 N climbs a distance x up the ladder. The coefficient of static friction between the ladder and the floor is 0.50. What is the maximum value of x for which the ladder will not slip?

A uniform ladder 12 meters long rests against a vertical frictionless wall, as shown in the figure. The ladder weighs 400 N and makes an angle θ = 51° with the floor. A man weighing 874 N climbs slowly up the ladder. When he is 78 m from the bottom of the ladder, it just starts to slip. What is the coefficient of static friction between the floor and the ladder?

A croquet mallet balances when suspended from its center of mass, as shown in the left part of the figure. If you cut the mallet into two pieces at its center of mass, as shown in the right part of the figure, how do the masses of the two pieces compare? (There could be more than one correct choice.)

A 7.0-kg pipe is hung from a steel wire that is 2.5 m long and has a diameter of 0.75 mm. Young's modulus for steel is 2.0 × 10¹¹ N/m². (a) By what distance does the wire stretch? (b) If the wire diameter were doubled, what would be the stretch?

A cable is 100-m long and has a cross-sectional area of 1.0 mm². A 1000-N force is applied to stretch the cable. Young's modulus for the cable is 1.0 × 10¹¹ N/m². How far does the cable stretch?

A very light ideal spring with a spring constant (force constant) of 2.5 N/cm pulls horizontally on an 18-kg box that is resting on a horizontal floor. The coefficient of static friction between the box and the floor is 0.65, and the coefficient of kinetic friction is 0.45. (a) How long is the spring just as the box is ready to move? (b) If the spring pulls the box along with a constant forward velocity of 1.75 m/s, how long is the spring? (c) How long is the spring if it pulls the box forward at a constant 2.75 m/s?

As one stretches a metal wire, which condition is reached first?

A store's sign has a mass of 20 kg and is 3.0 m long. It is uniform, so its center of gravity is at the center of the sign. It is supported horizontally by a small loose bolt attached to the wall at one end and by a wire at the other end, as shown in the figure. What is the magnitude of the net force that the bolt exerts on the sign?

A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the minimum distance, on the other side of the pivot, such that a 220-N force will make the child lift off the ground?

A 3.00-m-long ladder, weighing 200 N, leans against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.00 m away from the wall. The ladder is not completely uniform, so its center of gravity is 1.20 m from its base. What force of friction must the floor exert on the base of the ladder to prevent the ladder from sliding down?

A bridge piling has a cross-sectional area of 1.250 m² and supports a load of 1875 N. What is the stress on the column?

A meter stick balances at the 50.0-cm mark. If a mass of 50.0 g is placed at the 90.0-cm mark, the stick balances at the 61.3-cm mark. What is the mass of the meter stick?

A 50-kg air conditioner is placed on top of a concrete pad that is 20 cm thick and has a cross-sectional area of 3.0 m². What is the change in thickness of the pad caused by the air conditioner? Young's modulus for concrete is 2.3 × 10¹⁰ N/m².

A very light ideal spring of spring constant (force constant) 2.5 N/cm is 15 cm long when nothing is attached to it. It is now used to pull horizontally on a 12.5-kg box on a perfectly smooth horizontal floor. You observe that the box starts from rest and moves 96 cm during the first 1.6 s of its motion with constant acceleration. How long is the spring during this motion?

When a 125-kg piece of equipment is hung from a steel wire of diameter 6.00 mm, it stretches the wire by 4.00 mm. If instead the wire had a diameter of 3.00 mm, but all else were the same, by what distance would the same equipment stretch the wire?

A force of $30 \mathrm {~N}$ stretches a very light ideal spring $0.73 \mathrm {~m}$ from equilibrium. What is the force constant (spring constant) of the spring?

An 82-kg painter stands on a long horizontal board 1.55 m from one end. This 27-kg board is uniform, 5.5 m long, and supported at each end by vertical posts. (a) What is the magnitude of the total force provided by both posts? (b) With what force does the post that is closest to the painter push upward on the board?