Question

An object, previously at rest, slides `9 m` down a ramp, with an incline of `(pi)/3`, and then slides horizontally on the floor for another `25 m`. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?

Answer 1

`0.264211`

Explanation:

`d_r` Distance slided down on the ramp.
`alpha` Ramp incline.
`d_h` Distance slided horizontally.
`mu` Kinetic friction coefficient.
`m` Object mass.
`g` Gravity acceleration.

Equating

Potential Energy = Dissipated work against friction

`d_r sin alpha m g = m g cos alpha mu d_r + m g mu d_h`

or

`d_r sin alpha = cos alpha mu d_r + mu d_h`

then

`mu = (d_r sin alpha)/(cos alpha d_r+d_h) =(9 sqrt[3])/59 = 0.264211`