Assignment:
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.
Question 1. 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 .
Question 2. 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.
Question 3. 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.
Question 4. 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.