Question

A block of mass $m\text{kg}$ strikes an obstacle and moves at an angle of ${90}^{\circ }$ to its original direction. If its speed does not change, find the impulse acting on the block.

• A. $mv$
• B. $\sqrt{2}mv$
• C. $2mv$
• D. $0$

Answer 1

The correct option is B $\sqrt{2}mv$

Block was moving along $+vex-$ axis direction initially and after striking the obstacle, it moves along $+vey-$ axis direction.
i.e initial velocity $\overrightarrow{v_i}=v\hat{i}$
and final velocity, $\overrightarrow{v_f}=v\hat{j}$

Then, Impulse, $\overrightarrow{J}=m\Delta \overrightarrow{v}$
$\overrightarrow{J}=m(\overrightarrow{v_f}-\overrightarrow{v_i})=m(v\hat{j}-v\hat{i})$
$\Rightarrow |\overrightarrow{J}|=m\times \sqrt{v^2+v^2}$
$\therefore |\overrightarrow{J}|=\sqrt{2}mv$
$|\overrightarrow{J}|$ is the magnitude of impulse acting on the block.