college physics
posted by jessica .
Rather than rotate completely horizontally, a carousel rotates at an angle of 10° from horizontal, with a constant angular velocity of 1.571 RAD/s. A box is placed 1.5 m from the axis of rotation. What’s the minimum coefficient of static friction so the box will not slip?

acceleration down slope = w^2 R cos 10
so m a = m w^2 R cos 10
Force down slope = m g sin 10 + mu m g cos 10
so
g sin 10 + mu g cos 10 = w^2 R cos 10
g tan 10 + mu g = w^2 R
mu = ( w^2 r/g tan 10)
= 0.201
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