A block of mass m is positioned on another block of mass M , and the two-block system rests on a horizontal surface. When a constant horizontal force F is applied to the lower block, it generates an acceleration of F 2(m+M) in the system, and the two blocks travel together continuously. Calculate the frictional force acting on the smaller block.

Step-by-step solution

Given that the two blocks move together, they share the same acceleration. The acceleration of the system is given by: a = F 2(m+M) For the smaller block of mass m , the only horizontal force acting on it is the static frictional force f provided by the lower block. This frictional force is responsible for its acceleration. Applying Newton's second law to the smaller block: f = ma Substituting the value of acceleration a into the equation, we get: f = m [ F 2(m+M) ] f = mF 2(m+M)