First slide

Constraints

Question

For the pulley system shown in Fig. , each of the cables at A and B is given a velocity of 2 m $s^{- 1}$ in the direction of the arrow. Determine the upward velocity v of the load m.

Moderate

A

$1.5 m s^{- 1}$
B

$3 m s^{- 1}$
C

$6 m s^{- 1}$
D

$4.5 m s^{- 1}$

Solution

$v_{A}$ = 2m $s^{- 1}$ (towards right)
$V_{P_{1}} = \frac{V_{A}}{2} = 1 m s^{- 1}$ (upwards)
$V_{B} = 2 m s^{- 1}$ (towards left)
$2 V_{P_{2}} = V_{B} + V_{P_{1}}$
$V_{P_{2}} = \frac{V_{B} + V_{P_{1}}}{2} = \frac{2 + 1}{2} = 1.5 m s^{- 1}$

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