First slide

Constraints

Question

In the figure acceleration of A is 1 $m / s^{2}$ upwards, acceleration of B is 7 $m / s^{2}$ upwards and acceleration of C is 2 $m / s^{2}$ upwards. The acceleration of D will be

Moderate

A

7 $m / s^{2}$ downwards
B

2 $m / s^{2}$ downwards
C

10 $m / s^{2}$ downwards
D

8 $m / s^{2}$ downwards

Solution

Acceleration of pulley P
$a_{P} = \frac{a_{A} + a_{B}}{2} = \frac{1 + 7}{2} = 4 m / s^{2} (upward)$
Acceleration pulley Q will be 4 $m / s^{2} (upward)$
$a_{Q} = \frac{a_{D} - a_{C}}{2}$
4 = $\frac{a_{D} - 2}{2} \Rightarrow a_{D} = 10 m / s^{2} (↓)$

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