Answer to Question #306116 in Mechanics | Relativity for Wisdom

Question

A crate slide down a caugo ramp that is inclined at 37 degrees. If the coefficient of the friction between the crate and and the ramp is 0.15, what is the acceleration of the crate? what must the coefficient of the friction be in order for the crates to remains stationary and not to slide on the ramp?

Answer 1

Explanations & Calculations

• Apply F=ma down the incline for the motion of the crate and this happens after the maximum possible friction fails to hold no more.

$\qquad\qquad \begin{aligned} \small mg\sin\theta-f_{max}&=\small ma\\ \small mg\sin\theta-\mu.mg\cos\theta&=\small ma\\ \small a&=\small g(sin\theta-\mu.\cos\theta)\\ &=\small 9.8(\sin37-0.15\cos37)\\ &=\small 4.7\,ms^{-2} \end{aligned}$

• This happens at the maximum possible static \friction is acting on the crate.

$\qquad\qquad \begin{aligned} \small mg\sin\theta&=\small f_{max}\\ \small mg\sin37&=\small \mu.mg\cos37\\ \small \mu&=\small \tan37\\ &=\small 0.75 \end{aligned}$