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Physics chapter 9: Momentum and Its Conservation


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Momentum and Its Conservation

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Physics chapter 9: Momentum and Its Conservation

  1. 1. Momentum and Its Conservation Chapter 9
  2. 2. If you were to step in front of a fast moving train, would you be afraid of its momentum? A near miss!!!
  3. 3. Introduction  Well…. You should be afraid of the force it would apply to you! Momentum and force are directly related, but strictly speaking it’s the force that will hurt you.
  4. 4. Momentum and Impulse Momentum itself cannot be felt. It is a calculated (vector) quantity representing the “strength” or perhaps the “inertia” of an object’s motion  The quantity of momentum is represented in an equation by a letter “p”. The simplest formula for momentum is: p = mv (CES) (Units?) 
  5. 5. Momentum and Impulse Can a freight train and a feather have the same momentum? (In the absence of air) (In the presence of air?) Explain  Recall that (net) forces change the velocity of objects. F = ma F= m v t F t = m V (CES) Explanation of variables on next page. 
  6. 6. Momentum and Impulse “F t” (combined) is known as an impulse which causes an equivalent change in momentum “m v”  Let’s look at the units on both sides of this equation. Let’s also not get “hung up” on which symbols are bold and which aren’t in the book. As in the past, it is only bolding vector quantities. 
  7. 7. Momentum and Impulse What’s the formula for V?  V = Vf – Vi  F t = mvf – mvi = pf – pi (CES)  Example on overhead  Assign. P.233 #1-4 Don’t get hung up on the sketches. I always recommend them, but they don’t have to be in the detail they suggest. 
  8. 8. Newton’s 3rd Law and Momentum Recall that forces occur only as interactions between 2 or more objects. Newton’s 3rd Law states that forces occur in pairs (or multiples of 2), never alone. Any force is always accompanied by an equal and opposite (in direction) force.
  9. 9. (Continued) Remember this question? If in kicking a football there are equal and opposite forces, why does the ball move? Are there net forces? (Let’s refresh our memories.)  Do these forces cause equal and opposite accelerations? What about the change of momenta of the objects involved? 
  10. 10. The Law of Conservation of Momentum Recall that (net) forces applied over time (impulses) change momentum. Newton’s 3rd law and the Law of Conservation of Momentum are closely related to each other.  Football example: You kick the ball, the ball kicks you - Newton’s 3rd law.  Your foot slows down a little (loses “p”), the ball accelerates (gains “p”) 
  11. 11. Conservation of Momentum How is the momentum lost by your foot compared to the momentum gained by the ball?  The Law of Conservation of Momentum states that the total momentum within a defined system remains constant unless acted upon by an external force. (We’ll talk about what an external force is - later.) 
  12. 12. Conservation of Angular Momentum Tough question: Why is it that an ice skater spins faster when he/she pulls their arms in? Video Demo/volunteers for spinning on lab stool?  To comply with the law of conservation of momentum, of course. To explain this in a simple way recall that p = mv. The skater’s mass does not change at any time in this example -so let’s look at the velocity. 
  13. 13. Conservation of Momentum Recall V = d/t If the distance is decreased (circumference) then the time of the spin must decrease to keep “v” the same! This means they have to spin in less time (keeping the velocity the same). Here the skater is said to be conserving angular momentum. Bicycle wheel demo. Video  Let’s look at something a bit simpler - how this law applies to collisions in a straight line. 
  14. 14. Conservation of Momentum plost = pgained m vlost = m vgained If two objects are involved in a collision, then the sum of their momenta before and after are the same! (Does this make sense?) Mathematically: m1v1 + m2v2 = m1v1` + m2v2` (before) (after)
  15. 15. Cons of Momentum Example 
  16. 16. Conservation of Momentum 
  17. 17. Cons. of Momentum (cont) ndex.html(works only on site!)  Demo - collision balls/”Java Applets On Physics”  Video disk 3E Ch 31(1),32(2) 61(N) 63(N)64,66(N)67(2)68(1)  Sponge? Phys SimElastic Collisons 1 Dim. 
  18. 18. Internal and External Forces Recall that how a “system” or “frame of reference” (basically synonymous) is defined changes our interpretation. Let’s look at how this affects the game of pool.  Case 1 If we define our system to contain the cue ball and nothing else, what type of force does the cue stick represent?  An external force. The momentum of the cue ball changes as the law says it can. 
  19. 19. Internal and External Forces    Case 2 If we define our system to contain the cue ball and the cue stick (and the person holding it), then what type of force does the cue stick represent now? Does the total momentum change? The cue stick is an internal force. The total “p” does not change. The objects do accelerate in opposite directions, the amount of which is dictated by Newton’s 2nd law and their masses. Example p.157 old book (overhead and our formula) Video disk 1a77 Frame 49247
  20. 20. Internal Vs. External Force Example 
  21. 21. Additional Practice Problem 
  22. 22. Conservation of Momentum In 2 or 3 Dimensions     The LOCOM does not apply only to interactions in a straight line, but to all interactions! When two objects collide, they may go off in different directions, but the vector sum (Oh no!) of their resulting momenta will equal the sum of the momenta of the objects before the collision! Confused? How many of you play pool? p.159 (old book) overhead ions/Collisions.html Video - Mechanical Universe - Con. of “P
  23. 23. Chapter 9 Review Pp. 250-253  MC 33-36, 38-43 AC 46-50, 53-55  MP 56,57, 60, 65, 67, 69, 70, 72, 80  MR 83, 86, 