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
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#
