The
lower half of an inclined plane is rough the upper half being smooth a
particle is allowed to slide from the top and is brought to rest by
friction just as it reaches the bottom, find the ratio of the force of
friction to the weight of the particle intermes of the coefficient of
friction.
If it is at rest
plane angle T from horizontal
force down plane = m g sin T
force up plane = mu m g cos T
no acceleration so
mu m g cos T = m g sin T
or
mu = tan T