Question

A box of mass m is stacked on the top of a box of mass 3m. The surface of the table on which they sit is extremely smooth, but the surfaces of the boxes are not. If a force F is applied to the larger box, and the boxes do not move relative to each other, what is the static friction force on the less massive box?

Answer 1

Considering the force F applied to the large box,

$F=4m*a \to(1) \newline a=\frac{F}{4m} \newline$

Since the boxes does not move relative to each other.This frictional force is equal to the force acted on the smaller box(F'').

$F''=m*a \newline F''=m*\frac{F}{4m} \newline F''=\frac{F}{4} \newline$