Calculating the Initial Velocity of a Bullet: A Case Study in Momentum Conservation

Introduction to a Bullet Collision Problem

Consider a scenario where a bullet of a specific mass is fired into a block of metal, and the block is free to move. Following the impact, both the bullet and the block have a combined velocity of 70 m/s. The key question is to find the initial velocity of the bullet before the impact. This problem is a classic application of momentum conservation in physics.

Concept of Momentum and Its Conservation

Momentum is a measurement involving the quantity of motion of an object, calculated as the product of the object's mass and velocity. When bodies collide, if no external forces act on the system, the total momentum before the collision is equal to the total momentum after the collision; this is the principle of momentum conservation.

The Problem Statement

A bullet of mass 7 grams is fired into a block of metal weighing 7 kilograms. After the impact, the combined velocity of the bullet and the block is 70 m/s.

Using the formula for momentum, we can set up the equation for the conservation of momentum:

Pbefore.

Pbefore mbullet Vbullet mblock Vblock

Pbefore 0.007 kg Vbullet 0 kg Vblock (since the block is initially at rest)

Post-Impact Scenario

After the impact:

Pafter.

Pafter (mbullet mblock) Vall

Pafter (0.007 kg 7 kg) × 70 m/s

Pafter 7.007 kg × 70 m/s

Calculating the Initial Velocity of the Bullet

Setting the equations for Pbefore and Pafter equal to each other to apply the principle of momentum conservation:

0.007 kg Vbullet 0 kg Vblock 7.007 kg × 70 m/s

0.007 Vbullet 490.49 kg-m/s

Vbullet 490.49 / 0.007

Vbullet 70,070 m/s

Verification and Conclusion

Based on the calculation, the initial velocity of the bullet must be 70,070 m/s. This approach correctly follows the conservation of momentum and mathematical accuracy. The calculations have been verified multiple times, and the answer appears to be accurate. If the book or any other source provides a different answer, it's worth considering the possibility of errors in the reference material.

Key Takeaways

The conservation of momentum is a fundamental principle in physics. The initial velocity of the bullet in this scenario is 70,070 m/s. Problem-solving in physics often involves combining multiple concepts and rigorous calculations.

By understanding and applying the principles of momentum and conservation, one can accurately solve complex physics problems. For further discussion or to clarify any doubts, feel free to explore more resources or seek assistance from experts.