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More with momentum and Conservation of momentum

More with momentum and Conservation of momentum. A quick thought. A glass plate is dropped, would the impulse be greater if it fell on a concrete floor or a carpeted floor? In both cases the impulse would be the same (assuming it stopped upon impact) because the change in momentum is the same.

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More with momentum and Conservation of momentum

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  1. More with momentum and Conservation of momentum

  2. A quick thought • A glass plate is dropped, would the impulse be greater if it fell on a concrete floor or a carpeted floor? • In both cases the impulse would be the same (assuming it stopped upon impact) because the change in momentum is the same. • The carpeted floor would have a higher time of impact (therefore a smaller force), but an equal impulse to the concrete floor.

  3. What if it doesn’t stop upon impact • Two balls of equal mass are dropped from the same height. Upon hitting the ground, one bounces the other does not. Which ball will feel a greater impulse? • The ball that bounces • Impulse causes a change in momentum, that ball that bounces has a larger change in velocity, than the one that stops.

  4. Another thought on Newton’s third law, momentum, impulse and friction • In the winter, several years ago I was stuck behind a Camaro spinning its wheels on the ice. • Why couldn’t it go forward? • Very little friction between its tires and the ground. Cars use friction to move, the tire pushes on the ground, and it pushes on the car. • The coefficient of friction was very low and the weight of the car was very small in the rear end. • Fr =Fnμk

  5. Quick tidbit about most sports cars • Most of the weight of any car is in the front end (engine, transmission etc.) the only thing in the back is a trunk (low weight if its empty). • Sports cars are normally rear wheel drive meaning all power comes from the back tires, the front tires do not apply any force. • Sandbags in the trunk increase the weight in the rear end of the car and increase the friction on those tires.

  6. Back to the Camaro on ice • I got out to push it. I pushed and went backwards the car went nowhere (it did move but it was too small to notice) Why? • Mass, friction and impulse • Friction between my feet and the ground was also small, and when Newton’s 3rd law kicked in (instantly) I went backwards. The car had a much greater mass than me so it went (almost) nowhere.

  7. Where impulse fits in • Any force will cause an acceleration, but unless the force is huge it has to be for a sustained period of time to cause a (observable) change in motion (momentum). • I could only push for a fraction of a second before Newton’s 3rd law pushed me off of the car. I had to find a way to push the car over a period of time (impulse) to give it a forward velocity (momentum) • Ft = mv

  8. How I moved it • No, she did not want me to crack her new Camaro’s bumper with mine, so pushing her car with mine was out. • I pulled my car right behind hers and pushed her car with my foot on my bumper. What did this do? • Gave me more friction and mass (inertia). • Mass is obvious, friction increased because the weight of the car was much greater which increased the Fn (and Fr) which allowed me to push for several seconds.

  9. Momentum transfer • Momentum can be transferred from one object to another. • My forward momentum went from me to the Camaro. • After I pushed I had no momentum, and the car had momentum. • The net momentum of the system (myself my car and the Camaro) did NOT change.

  10. Law of Conservation of momentum • The net momentum of a system cannot change. • My initial forward momentum (and the momentum of the Camaro 0) equaled the final momentum of the car (and my final momentum 0) • If both objects were at rest to start, the forward momentum of what was pushed will be equal to the backward momentum of what pushed it. • Momentum can be transferred to the Earth.

  11. Representing this mathematically • The sum of the momenta of all objects to start will equal the sum of all final momenta. •  mvi =  mvf • The Greek letter  (sigma) means “the sum of” • so the sum of initial moment equals the sum of final momentum

  12. Bigger problems • If an 85 kg running back is running at 5.1 m/s and is hit (directly backwards) with 820 N force for 0.15 s, what will his velocity be? • -820N (.15s) = 85(v)- 85(5.1) • v = 3.7 m/s (forward)

  13. Homework • If a 92 kg running back is running at 5.1 m/s and is hit (directly backwards) by a linebacker with 410 N force for 2.1 s, what will his velocity be?

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