Elastic and Inelastic Collisions

Elastic Collision If 2 colliding objects are very hard and no heat is produced in the collision, KE is conserved as well as momentum ½ m 1 v ½ m 2 v 2 2 = ½ m 1 v 1 ’2 + ½ m 2 v 2 ’2 On a molecular level, most collisions are elastic, however on a large scale most are not totally elastic (some are very close) In elastic collisions, the 2 objects will rebound from one another

Solving Elastic Collision Problems Since 2 equations apply for elastic collisions, we can solve for two variables in a problem If the two equations are combined we also get a 3 rd equation In any elastic collision, the speed of the particles after the collision has the same magnitude but opposite direction as before (regardless of mass) v a - v b = -v a ’ + v b ’

Example A proton of mass 1.01 amu is traveling 3.6 x 10 4 m/s. It collides elastically with a He nucleus (4.0 amu) at rest. What are the velocities of each particle after the collision?

Inelastic Collisions Ones in which KE is not conserved The KE is not lost, just changed to some other form of energy such as heat KE is usually less after collisions In explosions, KE is usually greater Any collision where objects stick is elastic

Example A kg railroad car traveling at 24.0 m/s strikes an identical car at rest. The two cars couple together. How much of the car’s original KE was transformed to thermal energy?

Example The ballistic pendulum is a device used to measure the speed of a projectile, such as a bullet. If a projectile, of mass 5 g is fired into a large wooden block of mass 500 g which is suspended like a pendulum. If the pendulum raises to a height of 25 cm, what was the speed of the projectile?