1 / 36

Chapter 9

Impulse & Momentum. Chapter 9. Momentum. Momentum is what Newton called the “ quantity of motion ” of an object. Momentum. The momentum of an object: Depends on the object’s mass . Momentum is directly proportional to mass. Depends on the object’s velocity .

ashton
Download Presentation

Chapter 9

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Impulse & Momentum Chapter 9

  2. Momentum • Momentum is what Newton called the “quantity of motion” of an object.

  3. Momentum • The momentum of an object: • Depends on the object’s mass. • Momentum is directly proportional to mass. • Depends on the object’s velocity. • Momentum is directly proportional to velocity.

  4. Momentum • In symbols: p = mv p v m

  5. Momentum • Momentum is a vector quantity. • Common units of momentum: kg m/s

  6. Impulse • The impulse exerted on an object depends on: • The force acting on the object. • Impulse is directly proportional to force. • The time that the force acts. • Impulse is directly proportional to time.

  7. Impulse • In symbols: I = Ft I t F

  8. Impulse • Impulse is a vector quantity. • Common units of impulse: N s

  9. Impulse & Momentum • The impulse exerted on an object equals the object’s change in momentum.

  10. Impulse & Momentum • In symbols: I = Dp

  11. Conservation of Momentum • Since impulse = change in momentum, If no impulse is exerted on an object, the momentum of the object will not change.

  12. Conservation of Momentum • If no external forces act on a system, the total momentum of the system will not change. • Such a system is called an “isolated system”.

  13. Conservation of Momentum • Momentum is conserved in everyisolated system.

  14. Conservation of Momentum • Another way to think about it is: Internal forces can never change the total momentum of a system.

  15. Conservation of Momentum • In practice, for any event in an isolated system: • Momentumafter = Momentumbefore

  16. What does a rocket push against? • Cars push on the road • Boats push on the water • Propellers push against air • Jet engines push air through turbines, heat it, and push against the hot exhaust (air) • What can you push against in space?

  17. Momentum is conserved! • Before • After v = 0 so p = 0 M m v1 v2 m M pafter = Mv1 + mv2 = 0 as well so v1 = - (m/M) v2

  18. A Rocket Engine: The Principle • Burn Fuel to get hot gas • hot = thermally fast  more momentum • Shoot the gas out the tail end • Exploit momentum conservation to accelerate rocket

  19. A Rocket Engine: The Principle • Burn Fuel to get hot gas • Shoot the gas out the tail end • Exploit momentum conservation to accelerate rocket

  20. Rockets push against the inertia of the ejected gas! • Imagine standing on a sled throwing bricks. • Conservation of momentum, baby! • Each brick carries away momentum, adding to your own momentum • Can eventually get going faster than you can throw bricks! • In this case, a stationary observer views your thrown bricks as also traveling forward a bit, but not as fast as you are

  21. What counts? • The “figure of merit” for propellant is the momentum it carries off, mv. • It works best to get the propulsion moving as fast as possible before releasing it • Converting fuel to a hot gas gives the atoms speeds of around 6000 km/h! • Rockets often in stages: gets rid of “dead mass” • same momentum kick from propellant has greater impact on velocity of rocket if the rocket’s mass is reduced

  22. Spray Paint Example • Imagine you were stranded outside the space shuttle and needed to get back, and had only a can of spray paint. Are you better off throwing the can, or spraying out the contents? Why? • Note: Spray paint particles (and especially the gas propellant particles) leave the nozzle at 100-300 m/s (several hundred miles per hour)

  23. Going into orbit • Recall we approximated gravity as giving a const. acceleration at the Earth’s surface • It quickly reduces as we move away from the sphere of the earth • Imagine launching a succession of rockets upwards, at increasing speeds • The first few would fall back to Earth, but eventually one would escape the Earth’s gravitational pull and would break free • Escape velocity from the surface is 11.2 km/s

  24. Going into orbit, cont. • Now launch sideways from a mountaintop • If you achieve a speed v such that v2/r = g, the projectile would orbit the Earth at the surface! • How fast is this? R ~ 6400 km = 6.4106 m, so you’d need a speed of sqrt[(6.4106m)(10m/s2)] = sqrt (6.4107) m/s, so: • v  8000 m/s = 8 km/s = 28,800 km/hr ~ 18,000 mph

  25. 4 km/s: Not Fast Enough....

  26. 6 km/s: Almost Fast Enough....but not quite!

  27. 8 km/s: Not Too Fast, Nor Too Slow....Just Right

  28. 10 km/s: Faster Than Needed to Achieve Orbit

  29. Momentum

  30. Angular momentum • Angular momentum is a product of a rotating objects moment of inertia and angular velocity • L = I  • kg x m2/s • I = mr2 • Moment of Inertia = mass times the distance from the axis squared

  31. Angular momentum • Angular momentum is a product of a rotating objects moment of inertia and angular velocity • L = I  • kg x m2/s

  32. Conservation of Angular momentum • If no net external torque acts on a closed system, then its angular momentum does not change • Li = Lf

  33. Conservation of Angular momentum • If no net external torque acts on a closed system, then its angular momentum does not change • Li = Lf

  34. Conservation of Angular momentum • If no net external torque acts on a closed system, then its angular momentum does not change • Li = Lf

  35. Conservation of Angular momentum • If no net external torque acts on a closed system, then its angular momentum does not change • Li = Lf

  36. Torque

More Related