Physics acceleration question

Question

A 10-kg brick is being pulled by a string that is horizontal. The coefficient of friction is .32 and the tension force is 50N. What will be the acceleration of the brick?

Answer 1

This is a classic Dynamics problem. 1st step is to draw a free body diagram of the brick showing all forces. Vertically there are two forces, the normal force N pointing up and weight mg pointing down.

Using Newton's 2nd Law F_net = ma, Vertically: F_net = N-mg = ma (taking up to be positive). There is no movement vertically therefore no acceleration vertically so N-mg = 0 or N=mg.

Horizontally there are two forces, Tension T and friction f. Let's assume the brick is being pulled to the right. Friction always opposes motion so f points to the left.

Using Newton's 2nd Law F_net = ma again, Horizontally: F_net = T- f = ma (taking right to be positive). There is movement horizontally so there will be acceleration horizontally unless we are moving at constant velocity.

Solving for a and substituting µN for f we get a = (T-µN)/m = (T-µmg)/m = (50N-.32×10kg×9.8m/s²)/10kg = +1.864 m/s² where the positive sign means to the right or in the same direction as T