Question

A 1.0 kg box starts from rest and slides down a very rough inclined plane as shown below. Use energy principles to determine the coefficient of friction on the incline surface if its speed at the bottom is 2.78 m/s.

The box sits on a incline that is 0.5m above the ground on a 30 degree incline.

Answer 1

This is the diagram which I have drawn based on what is described in the problem. ( included a free body diagram too)

from the geometry, we can find length of incline.

sin 30 = 0.5 / L

L = 0.5 / sin 30

L = 1 m

so,

now, use energy conservation ( there is only potential energy at beginning and only kinetic energy at the end)

mgh_i - f * L = 1/2mv_f²

mgh_i - umgcos * L = 1/2mv_f²

cancel m on each side,

9.8 * 0.5 - u * 9.8 * cos 30 * 1 = 1/2 * 2.78²

1.0358 = u * 9.8 * cos 30 * 1

u = 0.122