A block of mass m is lowered with acceleration of 3g / 4 with the help of rope, from height h, find: ​

Question

A block of mass m is lowered with acceleration of \(\frac{3g}{4}\) with the help of rope, from height h, find:

(i) Work done by gravitation force on block.

(ii) Total work done on the block.

(iii) Work done on the block by rope.

Answer 1

(i) Work done by gravitational force on the block

\(W_1 = \vec F.\vec S\)

∵ Gravitational force (F = mg) and displacement (S = h) both are in same direction.

∴ θ = 0

∴ W₁ = FS cos 0° = FS = mgh

or W₁ = mgh

(ii) Net work done on the block,

\(W_2 = m\frac{3}{4}\ g\times h\)

(because acceleration is \(\frac{3}{4}\)g)

or \(W_2 = \frac{3}{4}\ mgh\)

(because rope resists the block from falling with acceleration g)

or W = \(\frac{3}{4}\ mgh\)