Answer to Question #150696 in Physics for Erica

Question

A crate with a mass of 20 kg is on a wooden plank which makes an angle of 45 degrees with the horizontal. If the coefficient of static friction between the crate and the plank is 0.18 will the crate slide down the plane by itself? Support your answer

Answer 1

First, let's remember that the coefficient of static friction can be found from the following equation:

$$\mu=\text{tan}\theta, \rightarrow \theta=\text{atan}\mu=10°.$$

We see that the coefficient of static friction between the crate and the plank of 0.18 corresponds to 10° incline. That is why the crate will slip.

If it slipped at angles higher than 45°, the coefficient of static friction would have to be

$$\mu=\text{tan}45°=1.$$