A bullet of mass 15 g has a speed of 400 m/s. What is its kinetic energy ? If the bullet strikes a thick target and is brought to rest in 2 cm, calculate the average net force acting on the bullet. What happens to the kinetic energy originally in the bullet ?

Explanation

To solve the problem step by step, we will first calculate the kinetic energy of the bullet and then determine the average net force acting on it when it strikes a target. Finally, we will discuss what happens to the kinetic energy originally in the bullet.

### Step 1: Calculate the Kinetic Energy of the Bullet

The formula for kinetic energy (KE) is given by:

\[ KE = \frac{1}{2} m v^2 \]

Where:
- \(m\) is the mass of the bullet in kilograms (kg)
- \(v\) is the speed of the bullet in meters per second (m/s)

**Given:**
- Mass of the bullet, \(m = 15 \text{ g} = \frac{15}{1000} \text{ kg} = 0.015 \text{ kg}\)
- Speed of the bullet, \(v = 400 \text{ m/s}\)

**Substituting the values into the formula:**

\[ KE = \frac{1}{2} \times 0.015 \times (400)^2 \]

Calculating \( (400)^2 \):

\[ (400)^2 = 160000 \]

Now substituting this back into the kinetic energy formula:

\[ KE = \frac{1}{2} \times 0.015 \times 160000 \]

Calculating \( \frac{1}{2} \times 0.015 = 0.0075 \):

\[ KE = 0.0075 \times 160000 = 1200 \text{ J} \]

### Step 2: Calculate the Average Net Force Acting on the Bullet

When the bullet strikes a thick target and is brought to rest, we can use the work-energy principle, which states that the work done on the bullet is equal to the change in kinetic energy.

**Work done (W) is given by:**

\[ W = F \times d \]

Where:
- \(F\) is the average net force acting on the bullet
- \(d\) is the distance over which the bullet is brought to rest (2 cm = 0.02 m)

Since the bullet comes to rest, the work done is equal to the initial kinetic energy:

\[ 1200 \text{ J} = F \times 0.02 \text{ m} \]

Now, we can solve for \(F\):

\[ F = \frac{1200}{0.02} \]

Calculating this gives:

\[ F = 60000 \text{ N} \]

### Step 3: What Happens to the Kinetic Energy Originally in the Bullet?

The kinetic energy originally in the bullet (1200 J) is transformed into other forms of energy when the bullet strikes the target. Primarily, this energy is converted into:

1. **Heat Energy**: Due to friction and deformation of the bullet and the target.
2. **Sound Energy**: The sound produced when the bullet strikes the target.
3. **Deformation Energy**: Some energy is used to deform the bullet and the target.

In summary, the kinetic energy is not lost but transformed into other forms of energy.

### Final Summary of Results:
- Kinetic Energy of the bullet: **1200 J**
- Average Net Force acting on the bullet: **60000 N**
- The kinetic energy is transformed into heat, sound, and deformation energy upon impact.

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