Exam 9: Static Equilibrium; Elasticity and Fracture

A 12-L volume of oil is subjected to pressure which produces a volume strain of $- 3.0 \times 10 ^ { - 4 }$ The bulk modulus of the oil is $6.0 \times 10 ^ { 9 } \mathrm {~Pa}$ and is independent of the pressure. The reduction in the volume of the oil in milliliters is closest to

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 bridge piling has a cross-sectional area of $1.250 \mathrm {~m} ^ { 2 }$ and supports a load of 1875 N. What is the stress on the column?

An irregularly shaped object that is 10 m long is placed with each end on a scale. If the scale on the right reads 96 N while the scale on the left reads 71 N, how far from the left end is the center of Gravity of this object?

A 50-kg load is suspended from a steel wire of diameter 1.0 mm and length 11.2 m. By what distance will the wire stretch? Young's modulus for steel is $2.0 \times 10 ^ { 11 } \mathrm {~Pa}$

A copper sphere that is 10 cm in diameter at an atmospheric pressure of $1.01 \times 10 ^ { 5 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ is put into a chamber where the pressure is $1.0 \times 10 ^ { 6 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ What is the change in the diameter of the sphere caused by this change in pressure? The bulk modulus for copper is $1.4 \times 10 ^ { 11 } \mathrm {~Pa}$

When the pressure applied to an unknown liquid is increased from $1.0 \times 10 ^ { 7 } \mathrm {~Pa}$ to $5.5 \times$ $10 ^ { 7 } \mathrm {~Pa}$ the volume of the liquid decreases by 0.70 % . Calculate the bulk modulus of the liquid.

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 Iadder will not slip?

A 25-kg television set rests on four rubber pads, each one having a height of 1.0 cm and a radius of 0.60 cm. A 200-N horizontal force is applied to the television set. How far does it move sideways due to the deformation of the rubber pads if the pads do not slide on the floor? The shear modulus of these rubber pads is $2.6 \times 10 ^ { 6 } \mathrm {~Pa}$

A shear force of 400 N is applied to one face of an aluminum cube having sides of 30 cm each. What is the resulting displacement of this face of the cube if the opposite face is held fixed? The shear modulus for aluminum is $2.5 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

A stepladder consists of two halves that are hinged at the top and connected by a tie rod which keeps the two halves from spreading apart. In this particular instance, the two halves are 2.5 m Iong, the tie rod is connected to the center of each half and is 70 cm long. An 800-N person stands 3/5 of the way up the stepladder, as shown in the figure. The ladder is light enough that we can neglect its weight, and it rests on an extremely smooth floor. What is the tension in the tie rod? (Note: To solve this problem, it is helpful to imagine cutting the ladder in half vertically and consider the forces and torques acting on each half of the ladder.)

A 25-kg piece of equipment can be hung by steel wires of length 1.00 m, 2.00 m, or 3.00 m. If all the wires have the same diameter, which one will stretch the greatest distance?

A light board that is 10 m long is supported by two sawhorses, one at one end of the board and a second at the midpoint. A 40-N object is placed between the two sawhorses, 3.0 m from the end and 2.0 m from the center. A second object, with a weight of 15 N, is placed on the supported end. What magnitude forces do the sawhorses exert on the board?

The graph in the figure shows the tensile stress as a function of the tensile strain in a certain wire. What does the slope of this graph give us for this wire?

A uniform 1200-N piece of medical apparatus that is 3.5 m long is suspended horizontally by two vertical wires at its ends. A small but dense 550-N weight is placed on the apparatus 2.0 m from one end, as shown in the figure. What are the tensions, A and B , in the two wires?

A 100-kg nonuniform boom that is 6.0 m long is loosely pinned at the pivot at P. A 600-kg concrete block is suspended from the end of the boom at A , as shown in the figure. The boom forms a $30 ^ { \circ }$ angle above the horizontal, and is supported by a 4.0 -m cable between points D and B . Point B is 4.0 m from P , and point D is 4.0 m above P . The center of mass of the boom is at point C , which is 2.0 m from P. Assume that all the quantities shown in the figure are accurate to two significant figures. What is the tension in the cable connected between points B and D?

Which of the following are SI units of Young's modulus? (There could be more than one correct choice.)

A piece of iron sinks to the bottom of a lake where the pressure is 21 times what it is at the surface of the lake. Which statement best describes what happens to the volume of that piece of iron?

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.

A wire of diameter 0.20 mm stretches by 0.20 % when a 6.28-N force is applied to it. What is Young's modulus for this wire?