Practice Problems: Calculating Final Velocity in One-Dimensional Inelastic Collisions

📚 Topic Summary

Inelastic collisions are collisions where kinetic energy is not conserved. This usually means some energy is converted into other forms, like heat or sound. A classic example is two objects sticking together after they collide. To solve these problems, we use the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision. This allows us to calculate the final velocity of the combined mass.

The key equation we'll be using is: $m_1v_{1i} + m_2v_{2i} = (m_1 + m_2)v_f$, where $m_1$ and $m_2$ are the masses of the objects, $v_{1i}$ and $v_{2i}$ are their initial velocities, and $v_f$ is the final velocity of the combined mass.

🧠 Part A: Vocabulary

Match the terms with their definitions:

1. Term: Momentum
2. Term: Inelastic Collision
3. Term: Conservation of Momentum
4. Term: Kinetic Energy
5. Term: Velocity

1. Definition: The energy of motion.
2. Definition: A collision where kinetic energy is not conserved.
3. Definition: Mass in motion; calculated as mass times velocity.
4. Definition: The rate at which an object changes its position.
5. Definition: The total momentum of a closed system remains constant if no external forces act on it.

(Match the terms above with the definitions. For example, write '1-C' if you think Momentum matches with 'The total momentum of a closed system...')

🧮 Part B: Fill in the Blanks

Complete the following sentences:

1. In an inelastic collision, __________ energy is not conserved.
2. The total __________ before a collision equals the total momentum after the collision.
3. If two objects __________ together after a collision, it is an inelastic collision.
4. The equation $m_1v_{1i} + m_2v_{2i} = (m_1 + m_2)v_f$ is used to calculate the __________ velocity in an inelastic collision.
5. __________ is a measure of mass in motion.

🤔 Part C: Critical Thinking

Explain, in your own words, why momentum is conserved in an inelastic collision, even though kinetic energy is not. Provide a real-world example to support your explanation.