Exam 12: Static Equilibrium; Elasticity and Fracture

FIGURE 12-7 -Assuming the lower arm has a mass of 2.8 kg and its CG is 12 cm from the elbow-joint pivot, how much force must the extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put (Fig. 12-7)?

FIGURE 12-1 -A 100-kg, 12.0-m long uniform beam is supported in equilibrium by two fulcrums as shown in Fig. 12-1. The left fulcrum is 1.00 m from the nearer end of the beam and the right fulcrum is 3.00 m from the nearer end of the beam. (a) What is the magnitude of the force of the left fulcrum on the beam? (b) What is the magnitude of the force of the right fulcrum on the beam?

A 0.600-mm diameter wire stretches 0.5% of its length when it is stretched with a tension of 20 N. What is the Young's modulus of this wire?

Compare and contrast tensile stress, compressive stress, and shear stress.

A truck is carrying a 120-kg refrigerator, which is 2.20 m tall and 85.0 cm wide has its center of mass at its geometrical center. The refrigerator is facing sideways and a short strip on the bed of the truck keeps the refrigerator from sliding. What is the maximum acceleration that the truck can have before the refrigerator begins to tip over?

A steel lift column in a service station is 4.0 m long and 0.20 m in diameter. Young's modulus for steel is 20 × 10¹⁰ N/m². By how much does the column shrink when a 5000-kg truck is on it?

FIGURE 12-5 -A 20.0-kg uniform plank is supported by the floor at one end and by a vertical rope at the other as shown in Fig. 12-5. A 50.0-kg mass person stands on the plank a distance three-fourths of the length plank from the end on the floor. (a) What is the tension in the rope? (b) What is the magnitude of the force of floor on the plank?

Two children are carrying a 2.00-m long uniform level board with a mass 5.00 kg, each supporting one end of the board. A 1.00-kg book is resting on the board a distance 1.20 m from one end of the board. What is the force applied by the child that is closer to the book to support the board?

An object whose center of gravity is above its base of support will be stable if a vertical line projected downward from the center of gravity falls within the base of support.

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

A uniform beam with a mass of 120 kg and a length of 5.0 m rests on two supports, one at the left edge and one 3.0 m from the left edge. How close to the right edge can a 68-kg person walk along the beam without causing it to tip over?

The maximum force that can be applied without breaking a material is called the breaking force.

An object in static equilibrium, if left undisturbed, will undergo no translational or rotational acceleration. However, if the object is displaced slightly, three outcomes are possible. List and explain each of these outcomes.

An object whose center of gravity is above its base of support will be unstable if a vertical line projected downward from the center of gravity falls outside of the base of support.

An object whose center of gravity is below its point of support, will be in neutral equilibrium.

What is the maximum length of steel cable that can hang vertically supported from one end of the cable? The Young's modulus of this steel is 2.10 × 10¹¹ N/m², the tensile strength of this steel is 7.4 × 10⁸ N/m², and the density of this steel is 7.6 × 10³ kg/m².

A mass of 1000 kg hangs at the end of a steel rod 5.0 m in length. The diameter of the rod is 0.80 cm and Young's modulus for the rod is 210,000 MN/m². What is the elongation of the rod?

A 3.00-m long plank of negligible mass has a 30.0-kg mass at one end and a 40.0-kg mass at the other end. How far from the 30.0-kg mass should a fulcrum be placed so that the plank is balanced?

If an object is in equilibrium, the net torque about any arbitrary axis must be zero.

A light board, 10 m long, is supported by two sawhorses, one at one edge of the board and a second at the midpoint. A 40-N weight is placed between the two sawhorses, 3.0 m from the edge and 2.0 m from the center. What forces are exerted by the sawhorses on the board?