A small block of mass m is placed at the left end of a larger block of mass M and length l , as shown in the figure. The system is capable of sliding on a horizontal road. It is given an initial velocity v towards the right. The coefficient of friction between the bigger block and the road is , while the coefficient of friction between the two blocks is /2 . Determine the time elapsed before the smaller block separat

Step-by-step solution

Let the right direction be positive. Both blocks initially move to the right with velocity v . The frictional force exerted by the road on the larger block M acts towards the left: f₁ = (M+m)g If both blocks were to move together, their common acceleration would be - g . The force required to keep the smaller block m moving with this acceleration is - mg . However, the maximum static friction available between the blocks is 2 mg . Since the required force exceeds the available friction, the blocks will slip relativ