To understand how to find the velocities of particles after a collision. 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 retain 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.
A) If the collision is elastic, what are the final velocities v_1 and v_2 of particles 1 and 2? Give the velocity v_1 of particle 1 followed by the velocity v_2 of particle 2, separated by a comma.
Express each velocity in terms of v.
B) Now suppose that the collision is perfectly inelastic. What are the velocities v_1 and v_2 of the two particles after the collision?
C) Give the velocity v_1 of particle 1 followed by the velocity v_2 of particle 2, separated by a comma. Express the velocities in terms of v.