Exam 9: Static Equilibrium; Elasticity and Fracture

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 $3.0 \mathrm {~m} ^ { 2 }$ What is the change in thickness of the pad caused by the air conditioner? Young's modulus for concrete is $2.3 \times 10 ^ { 10 } \mathrm {~N} / \mathrm { m } ^ { 2 }$

If the sum of the external forces on an object is zero, then the sum of the external torques on it must also be zero.

A 10-m uniform beam weighing 100 N is supported by two vertical ropes at its ends. If a 400-N person sits at a point 2.0 m from the left end of the beam, what is the tension in each rope?

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 $0.70 \times 10 ^ { 11 } \mathrm {~Pa}$ and for steel it is 2.0 x 10¹¹ Pa

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 $3.0 \times 10 ^ { 10 } \mathrm {~Pa}$ megapascals is closest to The shear stress on the block in

To determine the location of the center of mass (or center of gravity) of a car, the car is driven over a scale on a horizontal floor. When the front wheels are over the scale, the weight recorded by the scale is 5800 N, and when the rear wheels are over the scale, the scale reads 6500 N. The distance between the front and rear wheels is measured to be 3.20 m. How far behind the front wheels is the center of mass located?

A brass wire 2.0 m long and 2.0 mm in diameter supports a 10.0-kg fixture. By what distance did this fixture stretch the wire? Young's modulus for brass is $10 \times 1010 \mathrm {~N} / \mathrm { m } _ { 2 }$

Tensile strain is

If the sum of both the external torques and the external forces on an object is zero, then the object must be at rest.

A 5.00-m-long uniform ladder, weighing 200 N, rests against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.20 m away from the wall. The coefficient of static Friction between the ladder and the floor is 0.200. How far up the ladder, measured along the Ladder, can a 600-N person climb before the ladder begins to slip?

As shown in the figure, a uniform rectangular crate 0.40 m wide and 1.0 m tall sits on a horizontal surface. The crate weighs 460 N, and its center of gravity is at its geometric center. A horizontal force of magnitude F is applied at a distance h above the floor. Friction at the floor is great enough to prevent the crate from sliding. If h=0.69 m, what minimum value of F is required to make the crate start to tip over?

Two solid spheres are made from the same material, but one has twice the diameter of the other. Which sphere will have the greater bulk modulus?

A 25-kg television set rests on four rubber pads that are on the floor, each one having a height of 1.0 cm and a radius of 0.60 cm. A horizontal force is applied to the television set. When the pads are just at the point of sliding over the floor, how far has the television set moved sideways due to the deformation of the pads? The coefficient of static friction between the rubber and the floor is 1.0 and the shear modulus of these rubber pads is $2.6 \times 10 ^ { 6 } \mathrm {~Pa}$

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.)

Two blocks are made of the same material, but one has twice the volume of the other block. Which block will have the greater shear modulus?

If an object remains at rest, then the sum of both the external torques and the external forces on the object must be zero.

If the sum of the external torques on an object is zero, then the sum of the external forces on it must also be zero.

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

Which one of the following is an accurate statement?

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 $2.0 \times 10 ^ { 11 } \mathrm {~N} / \mathrm { m } ^ { 2 }$ (a) By what distance does the wire stretch? (b) If the wire diameter were doubled, what would be the stretch?