Question

There is a variable amount of friction between a block of mass m and a ramp at an angle θ above the horizontal. The kinetic and static coefficients of friction are equal but vary as µ=Ax, where x is measured along the ramp and x = 0 is the bottom of the ramp. The block is sent up the ramp with an initial speed v0, and comes to a stop somewhere on the ramp. In the following parts, take your “system” to be the block, the rough ramp, plus its interaction with the Earth through the gravitational field.

. If v0 is small, then the block will slide back down after it comes to rest. Find the smallest value of v0 such that after coming to rest at the top, the block does not slide back down.

Answer 1