Question

The upper portion of an inclined plane of inclination a is smooth and the lower portion is rough. A partical slide down from rest the top and just comes to rest at the foot . If the ratio of smooth length to rough length is `m:n`, find the coefficient of friction .

Answer 1

`2 a_(1) s_(1) = 2 a_(2) s_(2)` or `(a_(1))/( a_(2)) = (s_(2))/(s_(1)) = (n)/(m)`
`(g sin prop)/(mu g cos prop - g sin prop) = (m)/(n)`
Solving it,we get
`mu = ((m + n)/(m)) tan prop`