PHY Review Question

Question

At the end of a factory production line boxes start from rest and slide down a deg (horizontal) ramp that is 5.4 meters long.

Find a formula for the acceleration of the box down he ramp in terms of coefficient of kinetic friction.

If the boxes can spend no longer than 3.30 seconds on ramp what is max allowed coefficient of static friction between each box and ramp?

Answer 1

Hi Rebecca,

The wording is a bit funny, but I am going to assume the ramp is not horizontal, but at some angle θ above horizontal. Drawing a force diagram, we find a gravitational force of magnitude mg downward and a force of friction of magnitude μN in the direction opposing the direction of motion.

Decomposing the gravitational force into components parallel and perpendicular to the normal N, we find that

N = mg cosθ.

Then acceleration down the ramp can be computed as

ma = mg sinθ - μN = mg sin θ - μ mg cosθ.

dividing by m gives a formula for the acceleration. Then you can integrate twice to find the position as a function of time, and use the 3.3 second limit to find the max possible value of the friction.

I hope that helps! I am happy to help with the last part if needed, but this should at least get you off to a good start.