A block is resting at the top of a hill. If the coefficient of friction between the block and the hill is 0.9, what is the maximum angle of the slope before the block begins to slide?

Question

This is Physics 1. Please show your work and explain simply, I need help . Thanks!

Answer 1

Let the coordinate going down the ramp is x so positive x is down the ramp.

Let the weight of the block= mg

Let N = Normal force acting on the block from the ramp

Let u = the coefficient of friction = .9

Let a = the angle of the ramp

The forces on the block in the x direction is mgsin(a) - uN = 0 = mgsin(a) - umgcos(a) (In equilibrium)

Simplifying, sin(a) = ucos(a) or u = sin(a)/cos(a) = tan(a) = .9

Therefore, a = 41.99 degrees

So, at any angle above 41.99 degrees, the block will start to move