Question

A 4.00-kg box sits atop a 10.0-kg box on a horizontal table. The coefficient of kinetic friction between the two boxes and between the lower box and the table is 0.600, while the coefficient of static friction between these same surfaces is 0.800. A horizontal pull to the right is exerted on the lower box, as shown in the figure, and the boxes move together. What is the friction force on the UPPER box?

Answer 1

Newton’s second law for the system of two boxes in the x-direction is given by: 
F - f k = (m + M )a
F - µk (m + M )g = (m + M )a
⇒ a = (F/m + M) - µkg = (150N / (4kg+10kg)) - 0.6(9.8m/s² ) = 4.83m/s²

For the top box, we get fs = ma = 4kg x 4.83m/s² =19.3N