Calculate the force - pulley:

A string is passing over a smooth pulley. The string supports the mass m on one side which is to be pulled up with acceleration a. calculate the force T which must be applied at the end B of the string AB. Treat the block as a particle.

Solution

Figure (b) shows the free body diagram of the mass. The forces acting on it shall be the tension T in the string and the weight mg of the block. Since the block moves upwards, the inertia force F_i = - ma will be directed downwards. The block may be considered in equilibrium under the action of forces T, mg and ma.

          ∴ T - m g - m a = 0

or         T = m a + m g

                = m (a + g )

Therefore, the tension T to be applied to the end B shall equal to T = m (a + g ).