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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 4m board pivoted at the center. A 28kg child sits on one end of the board. Where should a 40kg child sit to balance the seesaw? Apply Σ τ = 0 about the pivot 2 × 28 = 40 d ; d = 1.4 m from pivot 3 · In Figure 1223, Misako is about to do a pushup. 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 τ = 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 60kg block on a 4m board as shown in Figure 1224. The mass of the board is 10 kg. Since Juan spends most of his time reading cookbooks, whereas Bettina regularly does pushups, 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 τ = 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 1225. 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 τ = 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 1226. 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 θ by μ s = tan θ . ( 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 = μ s F n ; F n = F c cos θ . For equilibrium, f s = F c sin θ . If f s = f s,max = F c sin θ = μ s F c cos θ , μ s = tan θ . ( b ) Taking long strides requires a large coefficient of static friction because θ is then large. ( c ) If μ s is small, i.e., there is ice on the surface, θ must be small to avoid slipping....
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This note was uploaded on 11/25/2010 for the course PHYSICS 4A taught by Professor Eduardo during the Spring '09 term at DeAnza College.
 Spring '09
 Eduardo
 Physics, Static Equilibrium

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