How to find energy due to friction?

Question

A 12.0 kg block is dragged over a rough, horizontal surface by a 71.0 N force acting at 20.0° above the horizontal. The block is displaced 5.00 m, and the coefficient of kinetic friction is 0.300. What is the increase in internal energy of the block-surface system due to friction?

Answer 1

First we need a free-body diagram for the block. The forces on the block are:

N, the normal force from the table, straight up
uN, the friction force from the table (where u is the coefficient of friction), to the left
mg, the force of gravity, straight down
71 N, the pulling force, to the right and up at a 20 degree angle

Solving Newton's Second Law for the vertical forces: there is no vertical acceleration, so

F = ma = 0 = N + 71 sin 20 - mg

Solve this equation for N

Now you know that the friction force is uN and therefore the work done by friction is uNd where d = 5.00 m. The work done by friction is equal to the change in internal energy of the block-surface system (that is, the surfaces get slightly warmer).