Question:

A pulley with two blocks of different masses are shown below.Find the acceleration in the pulley-block system.

Solution:

Acceleration in the pulley-block system:

Free body Diagram:

For 1 Kg block:

Force of gravity = m₁ g = 1 g

Tension in the string = T

For 3 Kg block :

Force of gravity = m₂ g = 3 g

Tension in the string = T

Applying Newton’s second law(F=ma) for the system:

$${m_1g-T=m_1a}$$

$${g-T=a}$$

This is equation (1)

$${m_2g-T=m_2a}$$

$${3g-T=3a}$$

This is equation (2)

Solving the above two equations

$${2g=4a}$$

$${a=\frac{g}{2}}$$

$${a=\frac{9.8}{2}}$$

$${a=4.9 \ \frac{m}{s^2}}$$

Aliter:

$${Acceleration=\frac{Net \ force}{Net \ mass}}$$

$${Acceleration=\frac{(3g-g)}{4}}$$

$${Acceleration =\frac{2g}{4}}$$

$${Acceleration =\frac{g}{2}}$$

$${a=\frac{9.8}{2}}$$

$${a=4.9 \ \frac{m}{s^2}}$$

Conclusion:

The acceleration in the pulley-block sytem is 4.9 ms^-2 .