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300_Physics ProblemsTechnical Physics

300_Physics ProblemsTechnical Physics - 302 P10.45 Rotation...

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302 Rotation of a Rigid Object About a Fixed Axis P10.45 (a) For the counterweight, F ma y y = becomes: 50 0 50 0 9 80 . . . = F H G I K J T a For the reel τ α = I reads TR I I a R = = α where I MR = = 1 2 0 093 8 2 . kg m 2 We substitute to eliminate the acceleration: 50 0 5 10 2 . . = F H G I K J T TR I T = 11 4 . N and a = = 50 0 11 4 5 10 7 57 . . . . m s 2 v v a x x f i f i 2 2 2 = + d i : v f = = 2 7 57 6 00 9 53 . . . a f m s FIG. P10.45 (b) Use conservation of energy for the system of the object, the reel, and the Earth: K U K U i f + = + a f a f : mgh mv I = + 1 2 1 2 2 2 ω 2 2 2 50 0 6 00 5 10 9 53 2 2 2 2 2 0 093 8 0 250 2 2 mgh mv I v R v m I R v mgh m I R = + F H G I K J = + F H G I K J = + = + = . . . . . . N m kg m s a fa f a f P10.46 Choose the zero gravitational potential energy at the level where the masses pass. K U K U E m v m v I m gh m gh v R v R v v f gf
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