Two boxes (m1 = 1kg and m2 = 3kg) and accelerated across a horizontal surface by a horizontal force F, applied to the left box. The magnitude of the frictional forces on the left box is 2N, and the magnitude of the frictional force on the right box is 4N. If the magnitude of F is 12N, what is the magnitude of the force on the right box by the left box?

F2 = 4.5N

Explanation:

This problem involves the application of newton's second law of motion we would treat both boxes as a composite body, combining their masses. The net force (the sum of all forces acting on the boxes) causes the mass M (both boxes) to move with an acceleration a. Three forces act on the boxes, F and the two frictional forces.

So

F - f1 - f2 = Ma

M = m1 + m2

Given m1 = 1kg and m2 = 3kg, F = 12N, f1 = 2N, f2 = 4N.

The frictional forces have a negative sign because they oppose the direction of motion.

So

12 - 2 - 4 = (1 + 3) * a

6 = 4a

a = 6/4 = 1.5m/s²

Each of the boxes moves the same acceleration a = 1.5m/s²

So the force on the right box is F2 = m2a = 3*1.5 = 4.5N