A ball of mass 2 kg is moving with velocity 20 m/sec strikes with the surface and rebounds with same speed, if time of contact is 0.1 sec then calculate average force on the ball.

Answer

To solve the problem, we need to calculate the average force exerted on the ball when it strikes the surface and rebounds. We can use the concept of momentum and Newton's second law of motion.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Mass of the ball (m) = 2 kg
- Initial velocity of the ball (u) = 20 m/s (moving towards the wall)
- Final velocity of the ball (v) = -20 m/s (moving away from the wall after rebounding)
- Time of contact (Δt) = 0.1 s

2. **Calculate Initial Momentum (p_initial):**
\[ p_{\text{initial}} = m \cdot u = 2 \, \text{kg} \cdot 20 \, \text{m/s} = 40 \, \text{kg m/s} \]

3. **Calculate Final Momentum (p_final):**
\[ p_{\text{final}} = m \cdot v = 2 \, \text{kg} \cdot (-20 \, \text{m/s}) = -40 \, \text{kg m/s} \]

4. **Calculate Change in Momentum (Δp):**
\[ \Delta p = p_{\text{final}} - p_{\text{initial}} = -40 \, \text{kg m/s} - 40 \, \text{kg m/s} = -80 \, \text{kg m/s} \]

5. **Calculate Average Force (F_avg):**
According to Newton's second law, the average force can be calculated as the rate of change of momentum:
\[ F_{\text{avg}} = \frac{\Delta p}{\Delta t} = \frac{-80 \, \text{kg m/s}}{0.1 \, \text{s}} = -800 \, \text{N} \]

6. **Interpret the Result:**
The negative sign indicates that the force is acting in the opposite direction to the initial motion of the ball (which is expected as it is hitting the wall). Therefore, the magnitude of the average force on the ball is:
\[ |F_{\text{avg}}| = 800 \, \text{N} \]

### Final Answer:
The average force on the ball is **800 N**.

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