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178_Physics ProblemsTechnical Physics

178_Physics ProblemsTechnical Physics - 180 P6.55 Circular...

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180 Circular Motion and Other Applications of Newton’s Laws P6.55 Take x -axis up the hill F ma T mg ma a T m g F ma T mg T mg a g g a g x x y y = + = = = + = = = = : sin sin sin sin : cos cos cos cos cos sin cos sin cos tan sin θ φ θ φ θ φ φ θ φ θ θ φ φ θ φ 0 b g *P6.56 (a) The speed of the bag is 2 7 46 38 1 23 π . . m s m s a f = . The total force on it must add to ma c = = 30 kg 1 23 7 46 6 12 2 b gb g . . . m s m N n mg f s a c x y FIG. P6.56 F ma f n F ma f n n f x x s y y s s = = = + = = : cos sin . : sin cos . cos . sin 20 20 6 12 20 20 30 9 8 0 20 6 12 20 N kg m s N 2 b g e j Substitute: f f f f s s s s sin cos sin . cos sin . . 20 20 20 6 12 20 20 294 2 92 294 16 8 106 2 + = = + = N N N N N a f a f (b) v = = 2 7 94 34 1 47 π . . m s m s a f ma c = = 30
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