Collisions

Completely elastic collision

If all of the kinetic energy is conserved, the collision is completely elastic.

Completely inelastic collision

If the objects stick together, the collision is completely inelastic. Some or all of the kinetic energy is lost.

Completely Elastic vs Inelastic

Partially inelastic collisionMost collision are neither completely elastic nor completely inelastic. Even if the objects involved bounce away from one another, some of the kinetic energy may be lost in the conversion process. (You can check mathematically!)

In this case, the collision can be considered to be partially inelastic.

Most of the energy lost is to heat, but some energy can be lost to sound or deformation of objects.

Inelastic collision: some or all of the kinetic energy is lost in the collision. Momentum is conserved.

Totally elastic collision: no kinetic energy is lost on impact. Elastic collisions conserve momentum and kinetic energy.

There are really no completely elastic collisions above the level of a few atoms but Silly putty and billiard balls are close.

If the initial speed = -final speed, the collision is elastic.

A 95g billiard ball traveling at 0.75m/s collides with a second ball at rest. The collision is completely elastic. What is the new speed of each ball?

• Momentum is conserved.• MaVai + MbVbi = MaVaf + MbVbf

• (.095)(0)+(.095)(.75)=(.095)Vaf +(.095)Vbf

• Cancel masses• (0) + (.75) = Vaf + Vbf

• We could rearrange the formula• Vaf = .75 - Vbf

Kinetic Energy is conserved.MaV2

ai + MbV2bi = MaV2

af + MbV2bf

2 2 2 2Cancel the masses and the 2’s(0) + (.75)2 = V2

af + V2bf

.56 = V2af + V2

bf

We could substitute the momentum formula in..56 = (.75 - Vbf )2 + V2

bf

.56 = V2bf -.75Vbf -.75Vbf + .56 + V2

bf

0 = 2V2bf – 1.5Vbf

0 = Vbf(2Vbf – 1.5)0 = Vbf and 0 = 2Vbf – 1.5Vbf = 0m/s and Vbf = .75m/s

That means that the moving ball hits the ball at rest and transfers all of its kinetic energy to that ball.

Ball A, mass 3.0 kg, is moving to the left at 2.5 m/s when it collides with ball B, mass 4.0 kg, moving to the right at 4.0 m/s. Ball A rebounds in the opposite direction with a speed of 2.0 m/s.a) Find the velocity of ball B after the collision.b) Is the collision completely elastic?

A 12kg ball traveling 2.4m/s hits a 36kg ball that is at rest. The collision is completely elastic. Find the new speed

of each ball after the collision.

• Momentum and kinetic energy are conserved. The new speeds are 1.2m/s and –1.2m/s.

A ball of mass 0.440kg moving with a speed of 8.10m/s collides head on with a 0.220kg ball at

rest. If the collision is perfectly elastic, what will be the velocities of the two balls after the collision?

• The answers: 2.8m/s & 10.8m/s

A 1.2kg ball traveling 3.6m/s hits a 4.8kg ball that is traveling toward

it at 1.2m/s. The collision is completely elastic. Find the new speeds for the balls.