Question

A mass of $100$ $g$ strikes the wall with speed $5$ $m/s$ at an angle as shown in figure and it rebounds with the same speed. If the contact time is $2\times {10}^{-3}$ $sec$. What is the force applied on the mass by the wall:

• A. $250\sqrt{3}$ to right
• B. $250$ $N$ to right
• C. $250\sqrt{3}$ $N$ to left
• D. $250$ $N$ to left

Answer 1

Answer: (C)

$250\sqrt{3}$ $N$ to left

$p_i=\frac{1}{2}\cos {30}^o(\uparrow )+\frac{1}{2}\sin {30}^o(\uparrow )$
$p_f=\frac{1}{2}\cos {30}^o(-\uparrow )+\frac{1}{2}\sin {30}^o(\uparrow )$
$\Delta p=\cos {30}^o(\uparrow )=\frac{\sqrt{3}}{2}$
$F=\frac{\Delta p}{\Delta t}=\frac{\sqrt{3}/2}{2\times {10}^{-3}}(-\uparrow )=\frac{100\sqrt{3}}{4}=250\sqrt{3}$ $N(-\uparrow )$ to the left.