Question

An object, previously at rest, slides `6 m` down a ramp, with an incline of `(3pi)/8`, and then slides horizontally on the floor for another `8 m`. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Answer 1

`mu = 0.409301`

Explanation:

Here `d_1 = 6`[m], `d_2 = 8`[m] and `alpha = 3 pi/8` and `mu` is the kinetic friction coefficient.

The initial potential energy is

`m g d_1 sin(alpha)`

The total dissiped work is given by

`tau_1+tau_2`

where `tau_1 = m g sin (alpha) mu d_1` and `tau_2=m g mu d_2`

so equating

`m g d_1 sin(alpha) = m g sin (alpha) mu d_1 + m g mu d_2`

Solving for `mu` gives

`mu = (d_1 sin(alpha))/(d_1 sin(alpha) + d_2) = 0.409301`