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Conservation of Momentum in Collisions

Learn about conservation of momentum and how it applies to collisions. Explore Newton's laws, impulse-momentum relationship, and calculations. Improve your understanding with reflective exercises.

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Conservation of Momentum in Collisions

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  1. Momentum Homework Review

  2. Conservation of Momentum Newton’s 2nd Law (a = F/m) tells us the an external force is needed to acceleration an object: If your car won’t start, you need someone to push it on the outside – it doesn’t help if you push on the dash!

  3. Conservation of Momentum Impulse-Momentum Relationship (Force)(time) = (mass)(velocity) What if there is no force? An external force is required for a change in momentum!

  4. Conservation of Momentum Newton’s 3rd Law: for every action, there is an equal and opposite reaction Force Force

  5. Conservation of Momentum How does this apply to momentum? The net force for the Cannon-Cannonball pair = 0 so the net momentum for the Cannon-Cannonball system = 0 Force / Momentum Force / Momentum

  6. Conservation of Momentum What does this mean? The momentum gained by the cannonball is equal to the momentum gained by the recoiling cannon (but the direction is opposite). No momentum is gained and no momentum is lost by the system.

  7. Law of Conservation of Momentum In the absence of an external force, the momentum of a system remains unchanged. Momentum is not conserved in a system that experiences an external net force. What is a system?

  8. Conservation of Momentum – What is a System? Consider the simple case of a pool ball striking one at rest. If the system is the ball at rest, then an external force acts on it (the other ball), and momentum is increased. Momentum for this ball is not conserved. System

  9. Conservation of Momentum – What is a System? Or if the system is the moving ball, then a reaction force acts on it when it strikes the ball at rest. This external force stops the ball in its tracks. Momentum for this ball is not conserved. System

  10. Conservation of Momentum – What is a System? Now consider the system to be both balls. For this system, no external force acts. For this system, net momentum doesn’t change, and momentum is conserved. It is merely transferred from one part of the system to the other without net change System

  11. CHECK YOURSELF If you toss a ball horizontally while standing on a skateboard, you’ll roll backward with the same amount of momentum that you have given to the ball. Will you roll backward if you go through the motions of tossing the ball but instead hold onto it?

  12. Collisions For collisions, the forces involved are internal forces – the object colliding are considered a system. Net momentum before collision = Net momentum after collision

  13. Collisions With the billiard ball example, when the moving ball hits the ball at rest, the first ball comes to a stop and the second ball moves with the initial velocity of the first ball. So we can compare the masses and velocities before and after the collision. (total mv) before = (total mv) after

  14. Collisions - Calculations Example: Suppose a block with a mass of 0.5 kg bumps into and sticks to a block that has a mass of 1.5 kg. If the speed of the block before the collision was 4 m/s, how fast will the two blocks move after the collision?

  15. Collisions - Calculations Mass 1 = 0.5 kg Velocity 1 = 4 m/s Mass 2 = 0.5 + 1.5 kg = 2 kg Velocity 2 = ? (0.5 kg)(4 m/s) = (2 kg)(? m/s) (2 kg m/s)/(2 kg) = ? m/s = 1 m/s

  16. How are you feeling about this concept? • Reflection How well do you understand Conservation of Momentum? Collision Calculations? What can you do to improve your understanding?

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