A bullet of mass 120 grams is fired into a target of mass 10 kg with velocity $$ 400 \mathrm{~m} / \mathrm{s} $$. If the target is free to move, the loss of kinetic energy would be approximately $$ \begin{array}{ll} ext { (1) } 9.5 \mathrm{kNm} & ext { (2) } 4.75 \mathrm{kNm} \ ext { (3) } 19 \mathrm{kNm} & ext { (4) } 0\end{array} $$

Question

A bullet of mass 120 grams is fired into a target of mass 10 kg with velocity $$ 400 \mathrm{~m} / \mathrm{s} $$. If the target is free to move, the loss of kinetic energy would be approximately $$ \begin{array}{ll}	ext { (1) } 9.5 \mathrm{kNm} & 	ext { (2) } 4.75 \mathrm{kNm} \ 	ext { (3) } 19 \mathrm{kNm} & 	ext { (4) } 0\end{array} $$

UpStudy AI · Accepted Answer

To determine the loss of kinetic energy when a bullet is fired into a target, we can follow these steps:

1. **Given Data:**
   - Mass of the bullet, $$ m_b = 120 \text{ grams} = 0.120 \text{ kg} $$
   - Velocity of the bullet, $$ v_b = 400 \text{ m/s} $$
   - Mass of the target, $$ M = 10 \text{ kg} $$

2. **Initial Kinetic Energy of the Bullet:**
   $$
   KE_{\text{initial}} = \frac{1}{2} m_b v_b^2 = \frac{1}{2} \times 0.120 \times (400)^2 = 9600 \text{ J} = 9.6 \text{ kJ}
   $$

3. **After the Collision:**
   - Assuming a perfectly inelastic collision, the bullet embeds into the target.
   - **Conservation of Momentum:**
     $$
     p_{\text{initial}} = m_b v_b = 0.120 \times 400 = 48 \text{ kg·m/s}
     $$
     $$
     v_{\text{final}} = \frac{p_{\text{initial}}}{M + m_b} = \frac{48}{10 + 0.120} \approx 4.752 \text{ m/s}
     $$
   
   - **Final Kinetic Energy of the Combined System:**
     $$
     KE_{\text{final}} = \frac{1}{2} (M + m_b) v_{\text{final}}^2 \approx \frac{1}{2} \times 10.120 \times (4.752)^2 \approx 114 \text{ J}
     $$

4. **Loss of Kinetic Energy:**
   $$
   \Delta KE = KE_{\text{initial}} - KE_{\text{final}} \approx 9600 \text{ J} - 114 \text{ J} \approx 9486 \text{ J} \approx 9.5 \text{ kJ}
   $$

**Conclusion:** The loss of kinetic energy is approximately **9.5 kJ**.

**Answer:**

Problem 1 Answer

The loss of kinetic energy is approximately 9.5 kNm.
The loss of kinetic energy is approximately 9.5 kNm.

A bullet of mass 120 grams is fired
into a target of mass 10 kg with
velocity . If the target is free to
move, the loss of kinetic energy would
be approximately

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A bullet of mass 120 grams is fired into a target of mass 10 kg with velocity . If the target is free to move, the loss of kinetic energy would be approximately