An object, previously at rest, slides #4 m# down a ramp, with an incline of #pi/12 #, 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?
The coefficient of kinetic friction is
At the top of the ramp, the object possesses potential energy.
At the bottom of the ramp, part of the potential energy is converted into kinetic energy and the work done by the frictional force.
The ramp is
The angle is
Let the speed at the bottom of the ramp be
On the horizontal part,
The initial velocity is
The final velocity is
The distance is
The deceleration is calculated with Newton's Second Law
We apply the equation of motion