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P112Sol7S06 - 6-34[Leg Presses 2Wby spring 2(80.0 J = 2 2 =...

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6-34 [Leg Presses] (a) First, find the spring constant k: W by you = - W by spring = 1 2 kx 2 - 0 k = 2W by spring x 2 = 2(80.0 J) (0.200 m) 2 = 4000 N/m Now, the force: F = kx = (4000 N/m)(0.200 m) = 800 N (b) W by you = - W by spring = 1 2 kx f 2 - 1 2 kx o 2 = 1 2 k(x f 2 - x o 2 ) = 1 2 (4000 N/m) [(0.400 m) 2 - (0.200 m) 2 ] = 240 J 7-12 [Tarzan and Jane] Take y = 0 to be at the bottom of Tarzan's swing. He starts at height y o = L - L cos45° and descends to final height y f = L - L cos30°. Use Cons. of Energy to find Tarzan's final speed: K o + U go = K f + U gf 0 + mgy o = 1 2 mv f 2 + mgy f Solve for v f = 2g(y o - y f ) = 2gL(cos30° - cos45°) = 2(9.8 m/s 2 )(20.0 m)(0.866 - 0.707) = 7.9 m/s This is pretty fast. Tarzan knocks Jane off her feet like a football player making a tackle. Ahh-ee- aahhh!!! 7-24 [Satellite Launcher] (a) The maximum acceleration occurs when the net force on the satellite is maximum. This is when the spring is fully compressed. Applying N’s 2 nd Law: F max = k x max = m a max (1) When the satellite is going at its maximum speed, all of the PE initially stored in the spring has been converted to KE of the satellite: _ k x max 2 = _ m v
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