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?

1 Answer
Jun 6, 2016

Answer:

#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#