First slide

Application of Newtons laws

Question

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

Difficult

A

$1.5 {ms}^{- 1}$
B

$3 {ms}^{- 1}$
C

$6 {ms}^{- 1}$
D

$4.5 {ms}^{- 1}$

Solution

$\begin{array}{l} v_{A} = 2 {ms}^{- 1} (towards right) \\ ∴ v_{P_{1}} = \frac{v_{A}}{2} = 1 {ms}^{- 1} (upwards) \\ v_{B} = 2 {ms}^{- 1} (t o w a r d s l e f t) \end{array}$
$Now 2 v_{P_{2}} = v_{B} + v_{P_{1}}$
$∴ v_{P_{2}} = \frac{v_{B} + v_{P_{1}}}{2} = \frac{2 + 1}{2} = 1.5 {ms}^{- 1}$

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