Question

A boy of mass 60 kg is holding a vertical rope, the rope breaks if the mass of 75 kg is suspended from it. What is the maximum acceleration of the boy with which it can climb the rope ?

Answer 1

Answer:

See below.

Explanation:

The rope has withstand a mass of 75 kg. The acceleration due to gravity is 9.8 m/s^2. Therefore the force it has withstand is,

$T = mg = 75 \times 9.8 = 735 N$

This force is nothing but the tension with the rope has hold. By considering that all the forces are in equilibrium,

$T + ma - mg = 0 \\ T + ma = mg \\ 735 + (60)a = 60 \times 9.8 \\ 735 - 588 = 60a$

On solving for a,

$\frac{147}{6} = 24.5$

Hence, at 24.5 m/s^2 acceleration, the tension will become 735 N which will break it.

Hope it helps.