A block of mass m sits on top of another block of mass M , and the entire system rests on a horizontal surface. A constant horizontal force F acting on the lower block results in an acceleration of F 2(m+M) for the system, where the two blocks consistently move together. Evaluate the work done by the force of friction on the smaller block by the larger block over a displacement d of the system.

Step-by-step solution

Given that the two blocks move together, they share the same acceleration. The acceleration of the system is given as: a = F 2(m+M) For the smaller block of mass m , the only horizontal force acting on it is the static friction force f exerted by the larger block M . This friction force is responsible for the acceleration of the smaller block. Using Newton's second law for the smaller block: f = ma Substituting the value of acceleration a : f = m ( F 2(m+M) ) = mF 2(m+M) The displacement of the system, and thus the