Question

A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 .if the acceleration of the system is g/8, then find the ratio of their masses.

Answer 1

Answer on Question #45256, Physics, Mechanics | Kinematics | Dynamics

A light string passing over a smooth light pulley connects two blocks of masses $m1$ and $m2$ . If the acceleration of the system is $g/8$ , then find the ratio of their masses.

Solution:

$W_{1} = m_{1}g$

$W_{1} = m_{2}g$

The equations of motion are:

$$m _ {1} a = m _ {1} g - T$$ $$m _ {2} a = T - m _ {2} g$$

The adding of two equations gives:

$$m _ {1} a + m _ {2} a = m _ {1} g - T + T - m _ {2} g$$ $$m _ {1} a + m _ {2} a = m _ {1} g - m _ {2} g = g \left(m _ {1} - m _ {2}\right)$$

Thus, the acceleration is

$$a = \frac {g (m _ {1} - m _ {2})}{m _ {1} + m _ {2}}$$

Let

$$\frac {m _ {1}}{m _ {2}} = x$$

Thus,

$$a = \frac {g (m _ {2} x - m _ {2})}{m _ {2} x + m _ {2}} = \frac {g (x - 1)}{(x + 1)}$$

From given

$$a = \frac {g}{8}$$ $$\frac {g}{8} = \frac {g (x - 1)}{(x + 1)}$$

or

$$- = \frac {x -}{x +}$$

or

$$x + = x -$$

or

$$9 = 7x$$

Thus,

$$x = \frac {9}{7}$$

Answer: $\frac{m_1}{m_2} = \frac{9}{7}$ .

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