Question

A couch with a mass of 100 kg is placed on an adjustable ramp connected to a truck. When one end of the ramp is raised, the couch begins to move downward. If the couch slides down the ramp with an acceleration of .7 meters per second when the ramps angle is 25 degrees, what is the coefficient of kinetic friction between the ramp and the couch? How do i figure this out?

Answer 1

component of weight down ramp = mg sin(theta)

friction up ramp = u mg cos(theta) where u is the coeff of friction

therefore, we have

mg sin(theta)- umg cos (theta) = ma

or a = g(sin(theta) - u cos(theta))

so, sub 25 deg for theta, 0.7m/s/s for a and 9.8m/s/s for g and get

u = 0.39