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Momentum

Momentum. the quantity of motion. § 8.1–8.2. What’s the point?. Nature keeps careful account of momentum. Think Question. Which process will require more time ?. Pulling as hard as you can to accelerate a little red wagon from rest to a speed of 1 m/s.

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Momentum

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  1. Momentum the quantity of motion § 8.1–8.2

  2. What’s the point? • Nature keeps careful account of momentum.

  3. Think Question Which process will require more time? • Pulling as hard as you can to accelerate a little red wagon from rest to a speed of 1 m/s. • Pulling as hard as you can to accelerate a horse trailer from rest to a speed of 1 m/s. • The two take the same amount of time.

  4. Think Question Which process will require more force? • Accelerating a little red wagon from rest to a speed of 1m/s in ten seconds • Accelerating a horse trailer from rest to a speed of 1m/s in ten seconds. • The two take the same force.

  5. Impulse = FDt where F Is net force Dt is duration Impulse Effect of a force over time Impulse is a vector.

  6. Think Question Two objects of different masses move at the same velocity. Which one is harder to stop? The light object. The massive object.

  7. Think Question Two objects with the same mass move different speeds. Which one is harder to stop? The fast object. The slow object.

  8. p = mv Momentum Formula momentum is a vector.

  9. Whiteboard Work Prove that when a net force F is applied to an object of mass m for a time Dt, its change in momentum is Dp = FDt

  10. Impulse–Momentum Theorem • Impulse = FDt. • FDt = maDt = mDv • So FDt = D(mv) = change in momentum

  11. dp F = dt Newton’s second law As Newton had it:

  12. Poll Question Which changes its momentum the most? • A moving object that stops when it hits a barrier. • A moving object that bounces back from a barrier. Hints: Momentum is a vector. Which receives the greater impulse?

  13. final p – initial p final p – initial p initial p initial p Dp Dp final p final p= 0 Rebound and Momentum

  14. Poll Question Which changes its kinetic energy the most? • A moving object that stops when it hits a barrier. • A moving object that bounces back from a barrier. Hints: Kinetic energy is a scalar. Which has the greater net work done?

  15. Conservation of Momentum Here today, somewhere tomorrow § 8.2

  16. Poll Question If a 0.25-g insect collides with a 1250-kg compact car, which experiences the greatest impulse in the collision? The insect. The car. It’s a tie. Insufficient information to answer. Hint: Remember Newton’s third law.

  17. Poll Question If a 0.25-g insect collides with a 1250-kg compact car, which experiences the greatest momentum change in the collision? The insect. The car. It’s a tie. Insufficient information to answer. Hint:Remember the impulse-momentum theorem.

  18. Conservation of Momentum • Newton’s first law: • no outside force • no change in v • thus no change in p • So an isolated object’s momentum never changes.

  19. ∑pi = ∑pf Conservation of Momentum • Newton’s third law: • interacting objects apply equal and opposite impulses to each other • they experience equal and opposite momentum changes • So the sum of their momenta remains the same.

  20. Conservation of Momentum The total momentum of an isolated system never changes.

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