First slide

Second law

Question

A ball of 0.5 kg collided with wall at 30° with the normal at the point of contact with the wall and bounced back elastically. The speed of ball was $12 {ms}^{- 1}$ . The contact remained for Is. What is the force applied by wall on ball? [JIPMER 2018]

Moderate

A

$12 \sqrt{3} N$
B

$\sqrt{3} N$
C

$6 \sqrt{3} N$
D

$3 \sqrt{3} N$

Solution

Given, $m = 0.5 kg, v = 12 {ms}^{- 1}, ∆ t = 1 s and θ = 30 °$
Force applied by wall on ball,
   $F = \frac{∆ p}{∆ t}$ or $F = \frac{{(p_{f})}_{H} - {(p_{i})}_{H}}{Δ t}$
$∵$ In this elastic collision, final and initial velocities will be same but direction changes
   ${(p_{f})}_{H} = mv cosθ$
and ${(p_{i})}_{H} = - mv cosθ$
$∴ F = \frac{m v \cos θ + m v \cos θ}{Δ t} = \frac{2 m v \cos θ}{Δ t}$
   $F = \frac{2 \times 0.5 \times 12 \times \cos 30 °}{1} = 6 \sqrt{3} N$

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