A bullet of mass 0.04 kg moving with a speed of 600 m/s penetrates a heavy wooden block. It stops after a penetration of 500 cm. The resistive force exerted by the block on the bullet is

Options

A. 1440 N
B. 1480 N
C. 270 N
D. 310 N

Answer

To solve the problem step by step, we will use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

### Step 1: Identify the given data
- Mass of the bullet, \( m = 0.04 \, \text{kg} \)
- Initial speed of the bullet, \( v_i = 600 \, \text{m/s} \)
- Final speed of the bullet, \( v_f = 0 \, \text{m/s} \) (since the bullet stops)
- Penetration distance, \( d = 500 \, \text{cm} = 5 \, \text{m} \)

### Step 2: Calculate the initial kinetic energy of the bullet
The initial kinetic energy (\( KE_i \)) can be calculated using the formula:
\[ KE_i = \frac{1}{2} m v_i^2 \]
Substituting the values:
\[ KE_i = \frac{1}{2} \times 0.04 \, \text{kg} \times (600 \, \text{m/s})^2 \]
\[ KE_i = \frac{1}{2} \times 0.04 \times 360000 \]
\[ KE_i = 0.02 \times 360000 = 7200 \, \text{J} \]

### Step 3: Calculate the final kinetic energy of the bullet
The final kinetic energy (\( KE_f \)) is zero since the bullet comes to a stop:
\[ KE_f = 0 \, \text{J} \]

### Step 4: Apply the work-energy theorem
According to the work-energy theorem:
\[ KE_f - KE_i = \text{Work done by the resistive force} \]
Substituting the values:
\[ 0 - 7200 = \text{Work done by the resistive force} \]
\[ \text{Work done by the resistive force} = -7200 \, \text{J} \]

### Step 5: Relate work done to the resistive force
The work done by the resistive force can also be expressed as:
\[ \text{Work} = F \cdot d \]
Where \( F \) is the resistive force and \( d \) is the distance penetrated. Rearranging gives:
\[ F = \frac{\text{Work}}{d} \]
Substituting the values:
\[ F = \frac{-7200 \, \text{J}}{5 \, \text{m}} \]
\[ F = -1440 \, \text{N} \]

### Step 6: Determine the magnitude of the resistive force
The magnitude of the resistive force is:
\[ |F| = 1440 \, \text{N} \]

### Final Answer
The resistive force exerted by the block on the bullet is **1440 N**.