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?

1 Answer
Feb 23, 2016

Answer:

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#