Exam 12: Static Equilibrium; Elasticity and Fracture

FIGURE 12-1 -A massive uniform beam is supported in equilibrium by two fulcrums as shown in Fig. 12-1. Which fulcrum applied the greater magnitude force to the beam?

A 25-kg wooden sign 3.0-m long by 2.2-m high is supported by two nails along its left edge, one at the bottom of the sign and the other at the top. The nails are on the same vertical line. Find the horizontal component of the force exerted by the upper nail.

FIGURE 12-6 -A 3.00-kg ball rests in a frictionless groove as shown in Fig. 12-6. (a) What is the normal force between the left side of the groove and the ball? (b) What is the normal force between the right side of the groove and the ball?

FIGURE 12-2 -A thick uniform beam is balanced on a pivot as shown in Fig. 12-2 where it is in equilibrium. Which type of equilibrium is this and why is it of that type?

A 55-cm steel rod has a diameter of 30 cm. The compressive strength of steel is 500 × 10⁶ N/m². What is the compression force that would break the rod?

A cable is 100-m long and has a cross-sectional area of 1 mm². A 1000-N force is applied to stretch the cable. The elastic modulus for the cable is 1.0 × 10¹¹ N/m². How far does it stretch?

A cone balanced on its small end is in

A meter stick balances at the 50.0-cm mark. If a mass of 50.0 g is placed at the 90.0-cm mark, the stick balances at the 61.3-cm mark. What is the mass of the meter stick?

The maximum elongation of a typical metal is reached at the breaking point.

Tightrope walkers often employ a long pole to help them retain their balance. What advantage is there to using a very flexible pole so that the ends droop?

A shear force of 400 N is applied to one face of an aluminum cube with sides of 30 cm. What is the resulting relative displacement? (The shear modulus for aluminum is 2.5 × 10¹⁰ N/m²)

Several forces act on an object at rest. It is known that the sum of the forces acting on the object is zero. Which statement is necessarily true?

A sphere hanging freely from a cord is in

If the net torque on an object is zero, does the the net force on the object also have to be zero?

A 120-kg refrigerator, 2.00 m tall and 85.0 cm wide has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.300. Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it won't tip before it begins to slide?

A non-uniform, 80-g, meter stick balances when the support is placed at the 51.0-cm mark. At what location on the stick should a 5.0-g tack be placed so that the stick will balance at the 50.0 cm mark?

The Leaning Tower of Pisa is 55 m tall and about 7.0 m in diameter. The top is 4.5 m off center. How much farther can it lean before it becomes unstable?

The tensile strength for a certain steel wire is 3000 MN/m². What is the maximum load that can be applied to a wire with a diameter of 3.0 mm made of this kind of steel?

Two people are lifting a 2.0-m wide, 80-kg, office desk by the ends. One side is heavier than the other, and it is found that the person exerting the larger force is exerting a vertical force of 500 N. How far from that person is the center of mass of the desk?

FIGURE 12-3 -An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two pillars 1.60 m apart, as shown in Fig. 12-3. (a) Find the force exerted by pillar A. (b) Find the force exerted by pillar B.