Exam 9: Static Equilibrium; Elasticity and Fracture

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

When a car is weighed, it is driven slowly on a horizontal floor over a scale that records a reading as the front wheels go over the scale, and then records a second reading as the rear wheels go over The scale. The weight of the car is equal to

As shown in the figure, a 10.0 m long bar is attached by a frictionless hinge to a wall and held horizontal by a light rope that makes an angle $\theta = 49 ^ { \circ }$ with the bar. The bar is uniform and weighs 66.5 N. What distance x from the hinge should a 10.0 kg mass be suspended for the tension in the rope to be 177 N?

Which one of the following would be expected to have the smallest bulk modulus?

Opposing shearing forces of 3000 N are applied to the $4.00 - \mathrm { cm } \times 5.00 - \mathrm { cm }$ faces of a metal block measuring $3.00 \mathrm {~cm} \times 4.00 \mathrm {~cm} \times 5.00 \mathrm {~cm}$ By what amount does the block become slanted? The shear modulus for this metal is $8.10 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

Two wires are made out of the same metal, but one wire is twice as long as the other wire. Which wire will have the greatest elastic modulus?

At a depth of 1030 m in Lake Baikal (a fresh water lake in Siberia), the pressure has increased by 100 atmospheres $\text { (to about } 10 ^ { 7 } \mathrm {~N} / \mathrm { m } ^ { 2 } \text { ). }$ By what volume has $1.0 \mathrm {~m} ^ { 3 }$ of water from the surface of the lake been compressed if it is forced down to this depth? The bulk modulus of water is $2.3 \times 10 ^ { 9 }$ $\text { Pa. }$

A wire that is 1.0 mm in diameter and 3.5 m long stretches 3.5 mm when an 8.0-kg tool is hung from it. (a) What is Young's modulus for the material from this wire is made? (b) What is the effective spring constant for the stretching wire?

A mobile is shown in the figure. The horizontal supports have negligible mass. Assume that all the numbers given in the figure are accurate to two significant figures. What mass M is required to balance the mobile?

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 er and by a wire at the other end, as shown in the figure. What is the magnitude of the net force th the bolt exerts on the sign?

A uniform rod weighs 40 N and is 1.0 m long. It is hinged to a wall at the left end, and held in a horizontal position at the right end by a vertical string of negligible weight, as shown in the figure. What is the magnitude of the torque due to the string about a horizontal axis that passes through the hinge and is perpendicular to the rod? The hinge is very small with negligible friction.

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

The base of a metal 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 this metal is $3.0 \times 10 ^ { 10 } \mathrm {~Pa}$ The displacement of the upper face, in the direction of the applied force is closest to

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 weight is placed between the two sawhorses, 3.0 m from the end and 2.0 m from the center. What magnitude forces do the sawhorses exert on the board?

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?

An athlete holds a 7.5-kg shot put in his hand with his lower arm horizontal, as shown in the figure. His lower arm has a mass of 2.8 kg and its center of gravity (or center of mass) is 12 cm from the elbow-joint pivot. How much force must the extensor muscle (which is $\overrightarrow { \mathrm { F } } _ { \mathrm { M } }$ in the figure) in the upper arm exert on the lower arm?

A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the magnitude of the minimum force, applied 0.30 m on the other side of the pivot, that is needed to make the Child lift off the ground?

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?

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

A large 75-kg lighting fixture can be hung from wires of identical size and shape made of aluminum, brass, or copper. The values of Young's modulus for these metals are $0.70 \times 10 ^ { 11 } \mathrm {~Pa}$ (aluminum), $0.91 \times 10 ^ { 11 } \text { (brass), and } 1.1 \times 10 ^ { 11 } \text { (copper) }$ Which wire would stretch the least distance?