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**Unformatted text preview: **CHAPTER 12 Static Equilibrium and Elasticity 1* · True or false: ( a ) Σ F = 0 is sufficient for static equilibrium to exist. ( b ) Σ F = 0 is necessary for static equilibrium to exist. ( c ) In static equilibrium, the net torque about any point is zero. ( d ) An object is in equilibrium only when there are no forces acting on it. ( a ) False ( b ) True ( c ) True ( d ) False 2 · A seesaw consists of a 4-m board pivoted at the center. A 28-kg child sits on one end of the board. Where should a 40-kg child sit to balance the seesaw? Apply Σ t = 0 about the pivot 2 × 28 = 40 d ; d = 1.4 m from pivot 3 · In Figure 12-23, Misako is about to do a push-up. Her center of gravity lies directly above point P on the floor, which is 0.9 m from her feet and 0.6 m from her hands. If her mass is 54 kg, what is the force exerted by the floor on her hands? Apply Σ t = 0 about her feet as a pivot 0.9 × 54 × 9.81 = F × 1.5 N . m; F = 318 N 4 · Juan and Bettina are carrying a 60-kg block on a 4-m board as shown in Figure 12-24. The mass of the board is 10 kg. Since Juan spends most of his time reading cookbooks, whereas Bettina regularly does push-ups, they place the block 2.5 m from Juan and 1.5 m from Bettina. Find the force in newtons exerted by each to carry the block. Apply Σ t = 0 about the right end of the board Apply Σ F = 0 (60 × 1.5 + 10 × 2) g = 4 × F J ; F J = 270 N 70 g = 270 N + F B ; F B = 417 N 5* · Misako wishes to measure the strength of her biceps muscle by exerting a force on a test strap as shown in Figure 12-25. The strap is 28 cm from the pivot point at the elbow, and her biceps muscle is attached at a point 5 cm from the pivot point. If the scale reads 18 N when she exerts her maximum force, what force is exerted by the biceps muscle? Apply Σ t = 0 about the pivot 28 × 18 = 5 × F ; F = 101 N 6 · A crutch is pressed against the sidewalk with a force F c along its own direction as in Figure 12-26. This force is balanced by the normal force F n and a frictional force f s . ( a ) Show that when the force of friction is at its maximum value, the coefficient of friction is related to the angle q by m s = tan q . ( b ) Explain how this result applies to the forces Chapter 12 Static Equilibrium and Elasticity on your foot when you are not using a crutch. ( c ) Why is it advantageous to take short steps when walking on ice? ( a ) f s,max = m s F n ; F n = F c cos q . For equilibrium, f s = F c sin q . If f s = f s,max = F c sin q = m s F c cos q , m s = tan q . ( b ) Taking long strides requires a large coefficient of static friction because q is then large. ( c ) If m s is small, i.e., there is ice on the surface, q must be small to avoid slipping. ...

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