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There are two main types of collisions that you will study: elastic and perfectly inelastic. In an elastic collision, kinetic energy is conserved. In a perfectly inelastic collision, the particles stick together and thus have the same velocity after the collision. There is actually a range of collision types, with elastic and perfectly inelastic at the extreme ends. These extreme cases are easier to solve than the in-between cases.

In this problem, we will look at one of these in-between cases after first working through some basic calculations related to elastic and perfectly inelastic collisions

Let two particles of equal mass m collide. Particle 1 has initial velocity v , directed to the right, and particle 2 is initially stationary.

QUESTION1)If the collision is elastic, what are the final velocities v1 and v2 of particles 1 and 2? Give the velocity of particle 1 followed by the velocity v2 of particle 2. Express each velocity in terms of v .

QUESTION2) Now suppose that the collision is perfectly inelastic. What are the velocities v1 and v2 of the two particles after the collision? Give the velocity v1 of particle 1 followed by the velocity v2 of particle 2. Express the velocities in terms of v.

QUESTION3)Now assume that the mass of particle 1 is 2m, while the mass of particle 2 remains m. If the collision is elastic, what are the final velocities v1 and v2 of particles 1 and 2? Give the velocity v1 of particle 1 followed by the velocity v2 of particle 2. Express the velocities in terms of v.

QUESTION4)Let the mass of particle 1 be m and the mass of particle 2 be 3m . If the collision is perfectly inelastic, what are the velocities of the two particles after the collision? Give the velocity v1 of particle 1 followed by the velocity v2 of particle 2;
Express the velocities in terms of v.

#### Solution Summary

The solution looks at momentum and collisions.

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