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141_Physics ProblemsTechnical Physics

141_Physics ProblemsTechnical Physics - Chapter 5*P5.53(a y...

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Chapter 5 143 *P5.53 (a) Situation A F ma F n mg F ma n mg x x A s y y = + = = + = : sin : cos µ θ θ 0 0 Eliminate n mg = cos θ to solve for F mg A s = sin cos θ μ θ a f . n mg cos θ mg sin θ y x f s F A FIG. P5.53(a) (b) Situation B F ma F n mg F ma F n mg x x B s y y B = + = = + = : cos sin : sin cos θ µ θ θ θ 0 0 Substitute n mg F B = + cos sin θ θ to find F mg F mg B s s B cos cos sin sin θ μ θ μ θ θ + + = 0 F mg B s s = + sin cos cos sin θ μ θ θ μ θ a f n mg cos θ mg sin θ y x f s F B FIG. P5.53(b) (c) F F A B = °− ° = = °+ ° = 2 9 8 25 0 16 25 5 44 19 6 0 278 25 0 16 25 5 59 kg m s N N N 2 . sin . cos . . . cos . sin . a f a f Student A need exert less force. (d) F F F B A A = °+ ° = cos . sin . 25 0 38 25 1 07 Student B need exert less force. P5.54 18 2 3
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