Question

A string is used to pull up a block of mass m vertically up by a distance h at a constant acceleration g/3 . The work done by the tension in the string is

Answer 1

k-mg =mg/3
kx =4mg/3

Answer 2

Given: Mass of block = m

          distance displaced = h

          angle between force and displacement = 0°

          acceleration = g/3

To find: the work done by the tension in the string

Solution: We know that, for work done:

                W = F.s cos ∅

In the question, it is evident that force is the tension in the string. Also, s is the h distance displaced. Putting the given values in the formula, we get:

                W = T. h. cos 0° __________(1)

Now, through the concept of pseudo force, we know that for acceleration and displacement of the body in the same direction, we have:

                T = m ( g + a )

Putting the given values, we obtain:

                T = m ( g + g/3)

                T = 4mg / 3 _________(2)

Putting (2) in (1), we obtain:

               W = 4mg/3 × h

               W = 4mgh/ 3.

Hence, the work done by the tension in the string is 4mgh/3.