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Exam 12: Equilibrium and Elasticity

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Question 1

Multiple Choice

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A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in ________ equilibrium with respect to rotation about the edge and in ________ equilibrium with respect to rotation about a horizontal axis that is perpendicular to the edge.

A) stable, stable
B) stable, unstable
C) unstable, stable
D) unstable, unstable
E) unstable, neutral

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Question 2

Multiple Choice

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A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its geometrical center, is:

A) in stable equilibrium
B) in unstable equilibrium
C) in neutral equilibrium
D) not in equilibrium
E) none of the above

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A

Question 3

Multiple Choice

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A cube with 2.0-cm sides is made of material with a bulk modulus of 4.7 * 10⁵ N/m². When it is subjected to a pressure of 2.0 *10⁵ Pa the length in cm of its any of its any of its sides is:

A horizontal beam of weight W is supported by a hinge and cable as shown. The force exerted on the beam by the hinge has a vertical component that must be:

A picture is to be hung from the ceiling by means of two wires. Order the following arrangements of the wires according to the tension in wire B, from least to greatest.

Two supports, made of the same material and initially of equal length, are 2.0 m apart. A stiff board with a length of 4.0 m and a mass of 10 kg is placed on the supports, with one support at the left end and the other at the midpoint. A block is placed on the board a distance of 0.50 m from left end.As a result the board is horizontal. The mass of the block is:

A certain wire stretches 0.90 cm when outward forces with magnitude F are applied to each end. The same forces are applied to a wire of the same material but with three times the diameter and three times the length. The second wire stretches:

A 240-N weight is hung from two ropes as shown. The tension in the horizontal rope has magnitude:

A picture P of weight W is hung by two strings as shown. The magnitude of the tension force of each string is T. The total upward pull of the strings on the picture is:

A uniform plank is 6.0 m long and weighs 80 N. It is balanced on a sawhorse at its center. An additional 160 N weight is now placed on the left end of the plank. To keep the plank balanced, it must be moved what distance to the right?

A shearing force of 50 N is applied to an aluminum rod with a length of 10 m, a cross-sectional area of 1.0 *10-⁵ m, and shear modulus of 2.5 *10¹⁰N/m^2. As a result the rod is sheared through a distance of:

Young's modulus is a proportionality constant that relates the force per unit area applied perpendicularly at the surface of an object to:

An 800-N man stands halfway up a 5.0 m ladder of negligible weight. The base of the ladder is 3.0 m from the wall as shown. Assuming that the wall-ladder contact is frictionless, the wall pushes against the ladder with a force of:

The pull P is just sufficient to keep the 14-N block and the weightless pulleys in equilibrium as shown. The tension T in the upper cable is:

The uniform rod shown below is held in place by the rope and wall. Suppose you know the weight of the rod and all dimensions. Then you can solve a single equation for the force exerted by the rope, provided you write expressions for the torques about the point:

The location of which of the following points within an object might depend on the orientation of the object?

A force of 5000 N is applied outwardly to each end of a 5.0-m long rod with a radius of 34.0 cm and a Young's modulus of 125 * 10⁸ N/m². The elongation of the rod is:

A picture can be hung on a wall in three different ways, as shown. The tension in the string is:

The 600-N ball shown is suspended on a string AB and rests against the frictionless vertical wall. The string makes an angle of 30 $\degree$ with the wall. The magnitude of the tension for of string is:

To determine if a rigid body is in equilibrium the vector sum of the gravitational forces acting on the particles of the body can be replaced by a single force acting at: