A block of mass m is released from rest on a rough inclined plane that makes an angle with the horizontal. The coefficient of kinetic friction between the block and the incline is . What is the kinetic energy of the block after it has slid a distance d down the plane?

Step-by-step solution

The forces doing work on the block as it slides down the incline are gravity and kinetic friction. The component of the gravitational force along the incline is mg . The work done by gravity over a distance d is W_g = mgd . The normal force on the block is N = mg . The kinetic friction force opposes the motion and has a magnitude f_k = N = mg . The work done by friction is W_f = -f_k d = - mgd . According to the work-energy theorem, the total work done on the block equals its change in kinetic energy. K = W_g + W_f