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Goal: To understand momentum

Goal: To understand momentum. Objectives: To Learn about What momentum is To learn about how to calculate Momentum in 2 dimensions To understand How is momentum changed? To understand the Conservation of momentum To learn about Why momentum is useful to understand.

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Goal: To understand momentum

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  1. Goal: To understand momentum Objectives: To Learn about What momentum is To learn about how to calculate Momentum in 2 dimensions To understand How is momentum changed? To understand the Conservation of momentum To learn about Why momentum is useful to understand. Tomorrow: To learn about applications to the conservation of momentum

  2. What is momentum • In reality momentum is quite simply a measure of your ability to create change. • Momentum = p = mv • Lets do a quick sample: • 1) A car with mass of 500 kg moves at a velocity of 20 m/s. What is the car’s momentum?

  3. Another example: • Two cars are headed towards one another. • The first car has 700 kg of mass and moves at a velocity of 20 m/s North • The 2nd car has 1400 kg of mass and moves at a velocity of 10 m/s South. • What is the combined momentum of the cars (yes momentum has direction)?

  4. Momentum in 2 dimensions… Each dimension has momentum. • So, you have to find the total momentum for each dimension separately. • Then at the end you can get a magnitude if you want, but usually it is more useful to keep them separate much like you keep a checking account separate from a savings account.

  5. Straight Foreward 2 D question • A car is heading North with a mass of 1000 kg and a velocity of 12 m/s. • A 2nd car is heading East with a mass of 750 kg and a velocity of 20 m/s. • Which car has a greater magnitude of momentum? • What is the combined magnitude of momentum for both cars combined

  6. Changing momentum • How do you change momentum? • You use what is called an “impulse”. • Impulse = change in momentum • Impulse = mass * change in velocity • Impulse = F * t • Note that F = ma • So, Impulse = m * (a * t) • What does acceleration * time equal?

  7. Example: • A car runs into a mailbox. • The mass of the mailbox is 10 kg and the mass of the car is 800 kg. • If the car imparts a 2000 N force to the mailbox for 0.4 seconds find: • A) The impulse on the mailbox • B) The new velocity of the mailbox (set impulse = to mass * change in velocity)? • C) What is the impulse the mailbox imparts on the car? (What, you have forgotten about Newton’s 3rd law already?) • D) How much does the car’s momentum change? • E) What is the net change in momentum (i.e. if you add the changes in momentum of the car and mailbox what do you get)?

  8. Conservation of momentum! • Momentum is almost always conserved in a collision. • In fact it is conserved for each dimension. • Total p before = Total p after • Quick question – will kinetic energy be conserved?

  9. Energy? • Sometimes kinetic energy is also conserved. • Collisions that conserve kinetic energy are called elastic collisions. • Collisions where energy is not conserved are called inelastic collisions.

  10. “Oooh, oooh, fender bender”The pips from that car commercial • In many collisions energy is transferred. • Energy is transferred to sound energy, heat energy, and used to crumple a car. • These collisions are always inelastic collisions. • So, if you get hit by a car, you want it to be an elastic collision! • You will fly faster and further, but the initial impact won’t use energy to bend and break things.

  11. Rear end crash • A speeding car of mass 800 kg attempting to elude the police crashes into a 600 kg car sitting parked at the intersection. • Ignoring brakes and friction, if the initial velocity of the speeding car is 50 m/s forward and the final velocity of the speeding car is 10 m/s forward then what will the final velocity of the other car be? • There are 2 ways to do this problem

  12. Head on collision • Car 1: 25 m/s East and a mass of 800 kg. • Car 2: 30 m/s West and a mass of 900 kg. • A) What is the net momentum of the two cars combined before the collision. • C) After the crash Car 1 moves West at a velocity of 5 m/s. What will the final velocity of car 1 be? Hint, total momentum

  13. T Bone! • Car 1: mass of 650 kg and headed North at 10 m/s • Car 2: mass of 750 kg and headed west at 5 m/s. • Car 1 T Bones Car 2 and car 1 comes to a complete stop. • A) Before the crash what are the momentums in the north and west directions? • B) After the crash how much momentum will car 1 have? • C) After the crash what is the north and west velocity of Car 2 (hint: will the west velocity change?) • D) What is the magnitude of the final velocity for car 2?

  14. If time: Ball off a wall • You bounce a 0.15 kg ball off of the wall. • The ball hits the wall at 20 m/s forward and when it bounces it returns (backward) at 80% of the SPEED of when it hit the wall. • A) What is the change in velocity for the ball (remember direction)? • B) What is the change in momentum? • C) If the ball is in contact with the wall for 0.6 seconds then what is the average force that the wall imparts to the ball? • D) What is the acceleration the wall gives the ball?

  15. Conclusion • Momentum = mass * velocity • Momentum is conserved! • Momentum is conserved in every direction! • If you run into something – or it runs into you – at high velocity – don’t bounce!

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