Exam 14: Static Equilibrium, Elasticity, and Fracture

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?

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). - The displacement of the y coordinate of the center of mass (from C to C') is

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?

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)

An object of mass m is suspended by two coplanar wires, as shown below. The tension in each wire has a magnitude given by

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). -The distance from C to C' is

Stress is proportional to strain means that

A horizontal uniform 1.20-N meter stick is held up by two vertical strings, one at the 20-cm mark and the other at the 60-cm mark. What is the tension in the string at the 60-cm mark?

A 20-m long steel wire (cross-section 1.0 cm², Young's modulus 2.0 × 10¹¹ N/m²), is subjected to a load of 25 000 N. How much will the wire stretch under the load?

A uniform 100-lb beam is held in a vertical position by a pin at its lower end and a cable at its upper end. A horizontal force (magnitude P) acts as shown in the figure. If P = 75 lb, what is the tension in the cable?

A uniform ladder 15 ft long is leaning against a frictionless wall at an angle of 53° above the horizontal. The weight of the ladder is 30 pounds. A 75-lb boy climbs 6.0-ft up the ladder. What is the magnitude of the friction force exerted on the ladder by the floor?

The 1560 kg solid steel door to a bank vault is 2.00 m high, 1.00-m wide and 10-cm thick. One hinge is 60.0 cm down from the top on the left-hand side of the door. The other hinge is 30.0 cm up from the bottom. What horizontal force, in what direction, does the door exert on the upper hinge?

A 25-ft long crane supported at its lower end by a pin is elevated by a horizontal cable as shown in the figure. A 250-lb load is suspended from the outer end of the crane. The center of gravity of the crane is 10 ft from the pin, and the crane weighs 200 lb. What is the tension in the horizontal cable?

The center of gravity of an object is at the same position as the center of mass when

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). -The displacement of the x coordinate of the center of mass (from C to C') is

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?

One of the curators at the art museum is tilting a large cylinder backward. At what angle θ will the cylinder of height h and radius r be in unstable equilibrium?

The free-body diagram below represents a 1500-kg car sitting on a 3000-kg bridge supported at its far ends. The car's position is three quarters of the length L from the left end of the bridge. Identify the one error in the torque equation below: ​ ​ ​

A non-uniform meter stick is found to balance on a knife edge at the 60-cm mark. Where is the center of gravity of the meter stick?

A horizontal uniform meter stick supported at the 50-cm mark has a mass of 0.50 kg hanging from it at the 20-cm mark and a 0.30-kg mass hanging from it at the 60-cm mark. Determine the position on the meter stick at which one would hang a third mass of 0.60 kg to keep the meter stick balanced.