First slide

Application of Newtons laws

Question

In the arrangement shown in the figure at a particular instant, the roller is coming down with a speed of 12 m s^-1and C is moving up with 4 ms^-1. At the same instant, it is also known that w.r.t. pulley P, blockr4 is moving down with speed 3 ms^-1. Determine the motion of block B (velocity) w.r.t. ground.

Moderate

A

4 ms^-1 in downward direction
B

3 ms^-1 in upward direction
C

7 ms^-1 in downward direction
D

7 ms^-1 in upward direction

Solution

Using constraint theory,
$\begin{array}{l} l_{1} + l_{2} + l_{3} = constant \\ \Rightarrow v_{1} + 2 v_{2} + v_{3} = 0 \end{array}$
Take downward as positive and upward as -ve.
$So 12 + 2 (- 4) + v_{3} = 0$
$\begin{matrix} v_{3} = velocity of pulley P = - 4 {ms}^{- 1} \\ = 4 {ms}^{- 1} in upward direction \end{matrix}$
$\begin{array}{l} {\vec{v}}_{A P} = - {\vec{v}}_{B P} \\ \Rightarrow {\vec{v}}_{A P} = - ({\vec{v}}_{B} - {\vec{v}}_{P}) \\ {\vec{v}}_{B} = {\vec{v}}_{P} - {\vec{v}}_{A P} = - 4 - (3) = - 7 {ms}^{- 1} \end{array}$
i.e., block B will moves up with speed 7 ms^-1.

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