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 m1v12 + ½ m2v2

2 = ½ m1v1’2 + ½ m2v2

’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 3rd 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)

va - vb = -va’ + vb’

Example

A proton of mass 1.01 amu is traveling 3.6 x 104 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 conservedThe KE is not lost, just changed to some

other form of energy such as heatKE is usually less after collisionsIn explosions, KE is usually greaterAny collision where objects stick is elastic

Example

A 10000 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?