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Collisions

Inelastic vs. Elastic Pg. 233 – 239 Pg. 240 - 248. Collisions. 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. Analyzing Collisions.

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Collisions

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  1. Inelastic vs. Elastic Pg. 233 – 239 Pg. 240 - 248 Collisions

  2. 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.

  3. 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

  4. note 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

  5. 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.

  6. 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.

  7. 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 )

  8. 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?

  9. 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

  10. Perfectly Inelastic Collisions Pg. 236 - 239

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

  12. note Perfectly Inelastic Collisions

  13. 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

  14. 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?

  15. Textbook • pg. 239, #2, 6, 7

  16. Perfectly Elastic Collisions Pg. 240 - 248

  17. 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

  18. note Perfectly Elastic Collisions

  19. copy • If object B is NOT stationary then we use the following formulas: Af ** fix the first formula on your formula sheet -- should say VAf not VBf

  20. Special Cases *copy • If MA = MB they will exchange velocities almost as if they passed through each other • If a lighter object collides with a much heaver, stationary object then the velocity of the lighter object is reversed and the heavier object remains stationary

  21. Practice

  22. Practice 3. • 3.

  23. Textbook • Pg. 248, #3, 5

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