223_Physics ProblemsTechnical Physics

223_Physics ProblemsTechnical Physics - Chapter 8 P8.18 In...

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Chapter 8 225 P8.18 In the swing down to the breaking point, energy is conserved: mgr mv cos θ = 1 2 2 at the breaking point consider radial forces F ma T mg m v r r r = + = max cos θ 2 Eliminate v r g 2 2 = cos θ T mg mg T mg T mg max max max cos cos cos cos cos . . . = = = F H G I K J = F H G G I K J J = ° θ θ θ θ θ 2 3 3 44 5 9 80 40 8 1 1 N 3 2.00 kg m s 2 b g e j *P8.19 (a) For a 5-m cord the spring constant is described by F kx = , mg k = 1 5 . m a f . For a longer cord of length L the stretch distance is longer so the spring constant is smaller in inverse proportion: k L mg mg L K U U K U U mgy mgy kx mg y y kx mg L x g s i g s f i f f i f f f = = + + = + + + + = + + = = 5 3 33 0 0 0 1 2 1 2 1 2 3 33 2 2 2 m 1.5 m . . e j e j d i initial final FIG. P8.19(a) here y y L x i f f = = + 55 m 55 0 1 2 3 33 55 0 55 0 5 04
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