Two blocks of masses m and 3m are placed in contact with each other on a smooth horizontal surface. In the first case, a horizontal force F is applied to the block of mass m to push the two-block system. In the second case, the same horizontal force F is applied to the block of mass 3m from the opposite direction to push the system. The ratio of the normal contact force between the blocks in the first case to that in

Step-by-step solution

Let the acceleration of the system in both cases be a . Since the total mass is 4m and the applied force is F , the acceleration is a = F 4m . In the first case, the force F is applied to mass m . The block of mass m pushes the block of mass 3m . The only horizontal force on the 3m block is the contact force N₁ . Applying Newton's second law to the 3m block: N₁ = 3m a = 3m ( F 4m ) = 3F 4 . In the second case, the force F is applied to mass 3m . The block of mass 3m pushes the block of mass m . The only horizontal