A bullet of mass 0.03 kg moving with a speed of 400m/s penerates 12 cm into fixed block of wood. Calculate the average force exerted by the wood on the bullet.

Explanation

To solve the problem of calculating the average force exerted by the wood on the bullet, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of the bullet (m) = 0.03 kg
- Initial speed of the bullet (u) = 400 m/s
- Final speed of the bullet (v) = 0 m/s (since it stops in the wood)
- Distance penetrated into the wood (s) = 12 cm = 0.12 m

2. **Calculate the initial kinetic energy of the bullet:**
The kinetic energy (KE) can be calculated using the formula:
\[ KE = \frac{1}{2} m v^2 \]
Substituting the values:
\[ KE = \frac{1}{2} \times 0.03 \, \text{kg} \times (400 \, \text{m/s})^2 \]
\[ KE = \frac{1}{2} \times 0.03 \times 160000 \]
\[ KE = 0.015 \times 160000 = 2400 \, \text{Joules} \]

3. **Use the work-energy theorem:**
According to the work-energy theorem, the work done (W) on the bullet by the wood is equal to the change in kinetic energy:
\[ W = KE_{\text{initial}} - KE_{\text{final}} \]
Since the bullet comes to a stop, the final kinetic energy is 0. Therefore:
\[ W = 2400 \, \text{Joules} - 0 = 2400 \, \text{Joules} \]

4. **Calculate the average force exerted by the wood:**
The work done is also given by the formula:
\[ W = F \cdot s \]
Where \( F \) is the average force and \( s \) is the distance penetrated. Rearranging this gives:
\[ F = \frac{W}{s} \]
Substituting the values:
\[ F = \frac{2400 \, \text{Joules}}{0.12 \, \text{m}} \]
\[ F = 20000 \, \text{N} \]

5. **Express the force in scientific notation:**
\[ F = 2 \times 10^4 \, \text{N} \]

### Final Answer:
The average force exerted by the wood on the bullet is \( 2 \times 10^4 \, \text{N} \).