Understanding the Concepts
* Momentum: Momentum is a measure of an object's mass in motion. It's calculated as mass (m) multiplied by velocity (v): p = mv
* Conservation of Momentum: In a closed system (where no external forces act), the total momentum before a collision equals the total momentum after the collision.
Applying the Concepts
1. Identify the system: The system consists of the bullet and the pop can.
2. Define initial and final states:
* Initial state: Before the collision, the bullet has momentum, and the pop can is at rest.
* Final state: After the collision, the bullet and pop can move together with a common velocity.
3. Set up the momentum conservation equation:
* Total initial momentum = Total final momentum
* m₁v₁ + m₂v₂ = (m₁ + m₂)v₃
where:
* m₁ = mass of the bullet (0.012 kg)
* v₁ = initial velocity of the bullet (400 m/s)
* m₂ = mass of the pop can (we'll need to find this)
* v₂ = initial velocity of the pop can (0 m/s)
* v₃ = final velocity of the bullet and pop can together (290 m/s)
4. Solve for the mass of the pop can (m₂):
* 0.012 kg * 400 m/s + 0 = (0.012 kg + m₂) * 290 m/s
* 4.8 kg*m/s = (0.012 kg + m₂) * 290 m/s
* m₂ = (4.8 kg*m/s / 290 m/s) - 0.012 kg
* m₂ ≈ 0.015 kg
5. The final answer: The pop can is moving at 290 m/s after the bullet emerges.
Important Note: This calculation assumes that the bullet and pop can move together as a single unit after the bullet emerges. In reality, there might be some energy lost to deformation of the pop can and heat, which would slightly reduce the final velocity.
