Question

A body of mass 100g moving with a velocity of 10m/s collides with a wall. If after the collision it moves in an opposite direction, calculate the change in Momentum

Answer 1

To calculate the change in momentum of the body when it collides with the wall, we will first find the initial and final momentum.

1. **Initial momentum (\( p_i \))**:
\[
p_i = m \cdot v_i
\]
Where:
- \( m = 100 \, \text{g} = 0.1 \, \text{kg} \) (converting grams to kilograms)
- \( v_i = 10 \, \text{m/s} \) (initial velocity)

\[
p_i = 0.1 \, \text{kg} \cdot 10 \, \text{m/s} = 1 \, \text{kg m/s}
\]

2. **Final momentum (\( p_f \))**:
After colliding with the wall, the body moves in the opposite direction. Therefore, its final velocity will be:
\[
v_f = -10 \, \text{m/s}
\]

Calculating the final momentum:
\[
p_f = m \cdot v_f = 0.1 \, \text{kg} \cdot (-10 \, \text{m/s}) = -1 \, \text{kg m/s}
\]

3. **Change in momentum (\( \Delta p \))**:
\[
\Delta p = p_f - p_i
\]
\[
\Delta p = -1 \, \text{kg m/s} - 1 \, \text{kg m/s} = -2 \, \text{kg m/s}
\]

Thus, the change in momentum is:
\[
\Delta p = -2 \, \text{kg m/s}
\]

The negative sign indicates that the momentum has changed direction. The magnitude of the change in momentum is \( 2 \, \text{kg m/s} \).