Question

An object, previously at rest, slides `3 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

0.098

Explanation:

By conservation of energy, all the gravitational potential energy converted by friction to heat.

`Delta "GPE" = mg (sin(pi/3)*3"m")`

`"Work done by friction" = Sigma ("Friction" * "distance")`

`= mg cos(pi/3) mu(3"m") + mg mu(25"m")`

So, equating them gives

`mg (sin(pi/3)*3"m") = mgcos(pi/3) mu(3"m") + mg mu(25"m")`

`sin(pi/3) * 3"m" = mu(cos(pi/3)*(3"m") + (25"m"))`

`mu = frac{sin(pi/3) * 3"m"}{cos(pi/3)*(3"m") + (25"m")}`

`= frac{sqrt3/2*3"m"}{1/2*(3"m") + (25"m")}`

`~~ 0.098`