Question

With what force must a man pull on the rope to hold the system in equilibrium? 2 m M​

Answer 1

The force that must be applied on the rope to hold the system in equilibrium should be (m+M)g / 4.

• For a system to be in equilibrium, the net downward and the net upwards forces should be equal.
• The net downward force is due to the mass of the man and the mass of the plank. F downwards = mg + Mg = (m+M)g.
• Let the force applied by the man be F. The tension in the string held by the man will be T such that T = F.
• The net upward force is due to the tension produced in the string attached to the upper pulley. It is 4T (as shown in the FBD attached below).
• Equating the forces, 4F = (m+M)g

        or F = (m+M)g / 4