Answer to Question #150574 in Classical Mechanics for Jan Razz

Question

I have an experiment about computing the coefficient static friction of an object on an inclined plane. I had a piece of flat wood as the plane, and a plastic prism as the object. We were instructed to slowly incline the plane, and once the object starts moving, we should stop raising the plane. In my understanding, slowly inclining the plane will provide a more accurate maximum height of the inclined plane as the object finally moves down and exceeds the limit of its static friction. What will happen if I suddenly incline the plane? Will I yield the same result as inclining the plane slowly and what is/are the principle/s behind it?

Answer 1

Q: What will happen if I suddenly incline the plane? Will I yield the same result as inclining the plane slowly and what is/are the principle/s behind it?

A: No. If you incline the plane suddenly, you will accelerate the wooden block upward. Then, as soon as you stop inclining the plane, according to Newton's first law, the block will continue its motion upward. This will decrease the normal force. Decreased normal force will lead to smaller force of friction and smaller coefficient of static friction (since the famous equation $\mu=\text{tan}\theta$ was obtained for no inertia case using mass times g).