A block of mass m is placed upon another block of mass M , and the system rests on a horizontal surface as depicted in the figure. A constant horizontal force F exerted on the lower block yields an acceleration of F 2(m+M) for the system, with both blocks always moving together. Determine the coefficient of kinetic friction between the larger block and the horizontal surface.

Step-by-step solution

Since both blocks move together, they can be considered as a single system of total mass (M+m) . The normal force exerted by the horizontal surface on the system is N = (M+m)g . The kinetic friction force acting on the lower block from the surface is f_k = _k N = _k(M+m)g . Applying Newton's second law to the system in the horizontal direction: F - f_k = (M+m)a Substituting the given acceleration a = F 2(M+m) into the equation: F - _k(M+m)g = (M+m) ( F 2(M+m) ) F - _k(M+m)g = F 2 Rearranging the terms to solve for