**Unformatted text preview: **6.100: Use the WorkEnergy Theorem, W = KE , and integrate to find the work. 1 2 KE = 0 - mv0 and W = (-mg sin - mg cos )dx. 2 0 Then,
x Ax 2 W = - mg (sin + Ax cos )dx, W = -mg sin x + cos . 2 0 x Set W = KE. 1 2 Ax 2 - mv0 = -mg sin x + cos . 2 2 To eliminate x, note that the box comes to a rest when the force of static friction balances the component of the weight directed down the plane. So, mg sin = Ax mg cos ; solve this for x and substitute into the previous equation. sin x= . A cos Then,
2 sin A 1 2 sin sin + A cos cos , v0 = + g 2 A cos 2 2 and upon canceling factors and collecting terms, v0 = 3 g sin 2 . Or the box will remain A cos 2 stationary whenever v0 3 g sin 2 . A cos ...

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