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 of finding the resistive force exerted by the block on the bullet, we can use the work-energy theorem. Here's a step-by-step breakdown of the solution:

### Step 1: Identify the given values
- Mass of the bullet (m) = 0.04 kg
- Initial speed of the bullet (v) = 600 m/s
- Final speed of the bullet (v_f) = 0 m/s (since it stops)
- Penetration distance (d) = 500 cm = 5 m (convert cm to m)

### Step 2: Calculate the initial kinetic energy (KE_initial)
The initial kinetic energy of the bullet can be calculated using the formula:
\[ KE_{\text{initial}} = \frac{1}{2} m v^2 \]

Substituting the values:
\[ KE_{\text{initial}} = \frac{1}{2} \times 0.04 \, \text{kg} \times (600 \, \text{m/s})^2 \]
\[ KE_{\text{initial}} = \frac{1}{2} \times 0.04 \times 360000 \]
\[ KE_{\text{initial}} = 0.02 \times 360000 \]
\[ KE_{\text{initial}} = 7200 \, \text{J} \]

### Step 3: Apply the work-energy theorem
According to the work-energy theorem:
\[ \text{Change in kinetic energy} = \text{Work done} \]
Since the bullet comes to a stop, the final kinetic energy (KE_final) is 0. Thus:
\[ KE_{\text{final}} - KE_{\text{initial}} = \text{Work done} \]
\[ 0 - 7200 \, \text{J} = \text{Work done} \]
\[ \text{Work done} = -7200 \, \text{J} \]

### Step 4: Calculate the resistive force (F)
The work done by the resistive force can also be expressed as:
\[ \text{Work done} = F \times d \]
Where:
- F is the resistive force
- d is the distance penetrated (5 m)

Rearranging the equation to solve for F gives:
\[ F = \frac{\text{Work done}}{d} \]
Substituting the values:
\[ F = \frac{-7200 \, \text{J}}{5 \, \text{m}} \]
\[ F = -1440 \, \text{N} \]

### Step 5: Interpret the result
The negative sign indicates that the force is acting in the opposite direction to the motion of the bullet, which is expected for a resistive force. Therefore, 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**.

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