Collisions Inelastic vs. Elastic Pg. 233 – 239 Pg

Momentum vs. Energy All 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. Energy All 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 Collisions A 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 Collisions The 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

Perfectly Inelastic Collisions  We concluded that when objects collide, become deformed, and stick together, the collision is inelastic

Perfectly Inelastic Collisions note

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

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 Collisions note

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