Question

A 160 g cricket ball is moving with a speed of 20 m/s. What force is required to stop the ball in 0.2 seconds?

• A. \( -4 \, \text{N} \)
• B. \( -8 \, \text{N} \)
• C. \( -12 \, \text{N} \)
• D. \( -16 \, \text{N} \)

Hint:

To stop an object, use the impulse-momentum theorem: - Impulse \( J = F \times \Delta t \), - Change in momentum \( \Delta p = m \Delta v \), - Solve for the force \( F = \frac{\Delta p}{\Delta t} \).

Answer 1

The Correct Option is D

Step 1: Using the impulse-momentum theorem.
The impulse \( J \) is given by: \[ J = F \times \Delta t \] where \( F \) is the force and \( \Delta t = 0.2 \, \text{s} \) is the time taken to stop the ball. The change in momentum \( \Delta p \) is: \[ \Delta p = m \Delta v \] where \( m = 0.16 \, \text{kg} \) (since \( 160 \, \text{g} = 0.16 \, \text{kg} \)) and \( \Delta v = 20 - 0 = 20 \, \text{m/s} \). Thus, the change in momentum is: \[ \Delta p = 0.16 \times 20 = 3.2 \, \text{kg.m/s} \] Step 2: Finding the force.
From the impulse-momentum theorem: \[ F \times 0.2 = 3.2 \] \[ F = \frac{3.2}{0.2} = 16 \, \text{N} \] Since the force is applied to stop the ball, the force is negative: \[ F = -16 \, \text{N} \]