Question

Two weights connected by a lightweight string running over a pully is known as an Atwoods Machine. Determine the acceleration of the two masses of a simple Atwood’s machine, with one fixed pulley and two masses m1 and m2. (m1 > m2)
(Do free-body diagram first for each weight.)

Answer 1

Answer on Question #68035-Physics-Mechanics | Relativity

Two weights connected by a lightweight string running over a pully is known as an Atwoods Machine. Determine the acceleration of the two masses of a simple Atwood's machine, with one fixed pulley and two masses m1 and m2. (m1 > m2)

(Do free-body diagram first for each weight.)

Solution

A free-body diagram for first weight:

A free-body diagram for second weight:

$$\left\{ \begin{array}{l} m _ {1} a = m _ {1} g - T \\ m _ {2} a = T - m _ {2} g \end{array} \right.$$ $$(m _ {1} + m _ {2}) a = (m _ {1} - m _ {2}) g$$

The acceleration of the two masses of a simple Atwood's machine is

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

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