Exam 12: Static Equilibrium and Elasticity

If 1.0 m³ of concrete weighs 5 × 10⁴ N, what is the height of the tallest cylindrical concrete pillar that will not collapse under its own weight? (The compression strength of concrete is 1.7 × 10⁷ N/m²)

A uniform 120-lb beam is supported in a horizontal position by a pin and cable as shown in the figure. What is the magnitude of the force by the pin on the beam?

The diagrams below show forces applied to a wheel that weighs 20 N. The symbol W stands for the weight. In which diagram(s) is(are) the wheel in equilibrium?

The figure shows a uniform, horizontal beam (length = 10 m, mass = 25 kg) that is pivoted at the wall, with its far end supported by a cable that makes an angle of 51° with the horizontal. If a person (mass = 60 kg) stands 3.0 m from the pivot, what is the tension in the cable?

Pairs of forces of equal magnitude act on identical cylinders as shown in the figures. In which example is the cylinder in translational and rotational equilibrium?

For safety in climbing, a mountaineer uses a 50-m long nylon rope that is 1.0 cm in diameter. When supporting a 90-kg climber, the rope elongates 1.6 m. Find the Young's modulus for the rope material.

A uniform beam having a mass of 60 kg and a length of 2.8 m is held in place at its lower end by a pin. Its upper end leans against a vertical frictionless wall as shown in the figure. What is the magnitude of the force the pin exerts on the beam?

Stress is proportional to strain means that

The four tires of an automobile are inflated to a gauge pressure of 2.0 × 10⁵ N/m² (29 PSI). Each of the four tires has an area of 0.024 m² that is in contact with the ground. Determine the weight of the auto.

Find the minimum diameter of a steel wire 18 m long that will stretch no more than 9 mm when a load of 380 kg is hung on the lower end. (Y steel = 2.0 × 10¹¹ N/m²).

Exhibit 12-1 A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. Use this exhibit to answer the following question(s). -Refer to Exhibit 12-1. The displacement of the y coordinate of the center of mass (from C to C') is

John is carrying a shovelful of snow. The center of mass of the 3.00 kg of snow he is holding is 15.0 cm from the end of the shovel. He is pushing down on the opposite end of the shovel with one hand and holding it up 30.0 cm from that end with his other hand. Ignore the mass of the shovel. Sarah says that his hand pushing down on the shovel must be exerting a greater force than the hand pushing up. James says it is just the reverse. Which one, if either, is correct?

Exhibit 12-1 A square of side is removed from one corner of a square sandwich that has sides of length L. The center of mass of the remainder of the sandwich moves from C to C'. Use this exhibit to answer the following question(s). -Refer to Exhibit 12-1. The distance from C to C' is

How large a pressure increase (in ATM) must be applied to water if it is to be compressed in volume by 1.0%? The bulk modulus of water is 2.0 × 10⁹ N/m² and 1 ATM = 1.0 × 10⁵ N/m².