Collisions

Inelastic vs. ElasticPg. 233 – 239Pg. 240 - 248

Momentum vs. EnergyAll interactions conserve momentum.

They do not necessarily conserve kinetic energy.

Obvious example: Explosions

Kinetic energy before is zero.Kinetic energy after is non-zero.

Momentum vs. EnergyAll interactions conserve momentum.

They do not necessarily conserve kinetic energy.

Head-on collisions also do not conserve energy: the kinetic energy is transformed into work done on the car.

Analyzing Collisions This feature divides all collisions into two classes:

Collisions in which kinetic energy is conserved = elastic Collisions in which kinetic energy is not conserved = inelastic

Elastic Inelastic

Analysing Collisions Elastic collision

Collision in which momentum and kinetic energy are both conserved

Inelastic collision Collision in which momentum is conserved but not kinetic

energy

** you can determine whether a collision is elastic or inelastic by calculating both the kinetic energy before and after the collision. Since momentum is always conserved, the total kinetic energy before and after a collision are the same, the collision is elastic. If not, the collision is inelastic

note

Inelastic CollisionsA collision in which kinetic energy is lost is

called an inelastic collision.

A collision in which the maximum possible energy is lost is called a perfectly inelastic collision.

Completely Inelastic CollisionsThe maximum possible energy loss (if no work

is done on the objects) occurs when the two objects stick together after colliding so that they have the same final velocity.

Elastic or Inelastic? 1. A 0.50 kg object (A) is moving at 5.0 m/s

[E] when it collides, head-one, with a stationary 1.0 kg object (B). If the 0.50 kg rebounds directly backward at 1.2 m/s, was the collision elastic? (hint: you will need to first find the velocity of the 1.0 kg object after the collision )

Practice 2. Car A, with a mass of 1800 kg, was

travelling north at 46 km/h and car B, with a mass of 2500 km, was travelling east at 38 hm/h when they collided.

A) Would the cars be located more to the North or East B) Was the collision elastic or inelastic?

Perfectly Elastic & Inelastic Collisions Most real collisions fall somewhere between

elastic and inelastic However, it is useful to consider perfectly

elastic and perfectly inelastic collisions as ideal examples of Newton’s Laws

Perfectly Inelastic Collisions

Pg. 236 - 239

Perfectly Inelastic Collisions We concluded that when objects collide,

become deformed, and stick together, the collision is inelastic

Perfectly Inelastic Collisionsnote

Practice 1. The two objects shown collide head-

on and stick together in a perfectly inelastic collision. What is their combined velocity after the collision?

2. A CSI expert needed to find the velocity of a bullet fired from a gun. He fired a 5.50 g bullet into a ballistic pendulum with a bob that had a mass of 1.75 kg. The pendulum swung to a height of 12.5 cm as shown. What was the velocity of the bullet just before it hit and become embedded in the pendulum bob? (hint: start with conservation of energy and then use conservation of momentum)

V1+2 = -9.8 m/s

Vb = 500 m/s

3. A block of wood with a mass of 0.50 kg slides across the floor toward a 3.50 kg block of wood. Just before the collision, the small block is travelling at 3.15 m/s. Because some nails are sticking out of the blocks, the blocks stick together when they collide. Scratch marks on the flloor indicated that they slide for 2.63 m cm before coming to a stop. What was the magnitude of the force?

Textbook pg. 239, #2, 6, 7

Perfectly Elastic Collisions

Pg. 240 - 248

Perfectly Elastic Collisions As suspected, when hard objects such as billiard balls

collide, bounce off each other, and return to their original shape, they have undergone elastic collisions

Very few collisions are perfectly elastic, but in many cases, the loss of kinetic energy is so small that it can be neglected

Because both kinetic energy and momentum are conserved, an analysis of this type of collision yield two very useful equations

Perfectly Elastic Collisionsnote

Practice

Consider the two carts shown below. What do you suppose happens to the total mechanical energy during an elastic collision?

When the two gliders collide, the spring bumper compresses initially and then springs back to its original shape. This occurs because some of the kinetic energy of the moving gliders is converted into elastic potential energy in the spring bumper during the compression which is then converted back into kinetic energy during the rebound.

Elastic Collisions and Mechanical Energy

Practice 3. 3.

Textbook Pg. 248, #3, 5