1. Physics 218, Lecture XIV1 Physics 218 Lecture 14 Dr. David Toback

2. Physics 218, Lecture XIV2 Chapter 8: Momentum Want to deal with more complicated systems Collisions Explosions Newton’s laws still work, but we need some new ideas

3. Physics 218, Lecture XIV3

4. 4 Today’s Lecture Begin with a definition of Linear Momentum Then show that conservation of momentum helps us solve certain types of problems –Things colliding –Things exploding

5. Physics 218, Lecture XIV5 Definition of Linear Momentum Vector equation!

6. Physics 218, Lecture XIV6 Restating Newton’s Second Law “The rate of change of momentum of an object is equal to the net force applied to it” √ If we exert a net force on a body, the momentum of the body changes

7. Physics 218, Lecture XIV7 What if  F=0? If  F=0, then dp/dt = 0,  p = constant Momentum doesn’t change momentum before = momentum after

8. Physics 218, Lecture XIV8 Conservation of Momentum For a system, by Newton’s laws,  F=0  Conservation of Momentum Sum of all momentum before = momentum after True in X and Y directions separately!

9. Physics 218, Lecture XIV9 Problem Solving For Conservation of Momentum problems: 1.BEFORE and AFTER 2.Do X and Y Separately

10. Physics 218, Lecture XIV10 Before X Y

11. Physics 218, Lecture XIV11 After Y X

12. Physics 218, Lecture XIV12 So what? Momentum is useful when we don’t know anything about the forces Examples from everyday life: –When ice skating, if you push someone, why do you go backwards? –Why does a gun recoil when you shoot it?

13. Physics 218, Lecture XIV13 Everyday Experience? Question: Why do you go backwards when you push someone on the ice? Newton’s Law’s answer: When you exert a force on another person, then, by Newton’s law, the person exerts an equal and opposite force on you.

14. Physics 218, Lecture XIV14 Everyday Experience? Cont… Question: Why do you go backwards when you push someone on the ice? Momentum Conservation Answer: Before: –The system starts with zero momentum (nobody is moving) After: –The system ends with zero momentum. You and your friend move in opposite directions

15. Physics 218, Lecture XIV15 Simple Gun Example A gun of mass M G is sitting at rest with a bullet of mass M B inside it. You shoot the gun and the bullet comes out with a speed V at angle . What is the recoil velocity of the gun?

16. Physics 218, Lecture XIV16 Weird example Ball of mass m is dropped from a height h: What is the momentum before release? What is the momentum before it hits the ground? Is momentum conserved?

17. Physics 218, Lecture XIV17 What if we add the Earth? What is the force on the ball? What is the force on the earth? Is there any net force in this system? Is momentum conserved?  F=0, then dp/dt = 0, → p = constant

18. Physics 218, Lecture XIV18 Momentum for a system is Conserved Momentum is ALWAYS conserved for a SYSTEM, you just have to look at a big enough system to see it correctly. –Not conserved for a single ball A ball falling is not a big enough system. You need to consider what is making it fall. –Newton’s Law: For every action there is an equal and opposite reaction Add up all the momentums in the problem –The forcer and the forcee

19. Physics 218, Lecture XIV19 Energy and Momentum in Collisions Definitions: Elastic collision = kinetic energy is conserved Inelastic collision = kinetic energy is not conserved. Momentum conserved? Total Energy conserved?

20. Physics 218, Lecture XIV20 Inelastic Collisions By definition: Inelastic = mechanical energy not conserved = kinetic energy not conserved Inelastic Example: Two trains which collide and stick together

21. Physics 218, Lecture XIV21 Colliding Trains: 1 Dimension The train car on the left, mass m 1, is moving with speed V o when it collides with a stationary car of mass m 2. The two stick together. 1.What is their speed after the collision? 2.Show that this is inelastic

22. Physics 218, Lecture XIV22 Ballistic Pendulum A bullet of mass m and velocity V o plows into a block of wood with mass M which is part of a pendulum. How high, h, does the block of wood go? Is the collision elastic or inelastic?

23. Physics 218, Lecture XIV23 Bottom line: When to use Momentum When you don’t know the forces in the system When you are studying all of the pieces of the system which are doing the forcing Before and After Problems

24. Physics 218, Lecture XIV24 Coming up… Next time: Finish Chapter 8 Next week: –Start Chapter 9 on Rotation –Exam 2, Thursday October 26 th –Homework 7 due

25. Physics 218, Lecture XIV25

26. Physics 218, Lecture XIV26 Notes Exam coming up next time….: –Here. Usual class time: Covering: Exam 1 material, Chapter 3(9) Chapter 4(1-8), Chapter 5(1-3) Chapter 6(1-8), Chapter 7(1-4), Calculus 2 Today’s material NOT ON EXAM 5 Bonus points on the mini-practice exam II. Requires a 100 on all 10 math quizzes, all HW and HW quizzes up through and including Chapter 7

27. Physics 218, Lecture XIV27 Next time: Exam coming up next time….: –Here. Usual class time: Covering: Exam 1 material, Chapter 3(9) Chapter 4(1-8), Chapter 5(1-3) Chapter 6(1-8), Chapter 7(1-4), Calculus 2 5 bonus points for getting a 100 on mini-practice exam II –Must complete everything to Chap 7. Reading for next lecture: –Rest of Chapter 9 on Momentum –Reading was due today, but I’ll grant an extension. Questions: 1 & 14

28. Physics 218, Lecture XIV28 Head On Collision A ball of mass m 1 collides head on (elastically) with a second ball at rest and rebounds (goes in the opposite direction) with speed equal to ¼ of its original speed. What is the mass of the second ball m 2 ?

29. Physics 218, Lecture XIV29 Next time: Exam Thursday –Extra credit if you have 100’s on all HW’s, HW quizzes and math quizzes before the exam Reading for Tuesday: –Rest of Chapter 9 on Momentum

30. Physics 218, Lecture XIV30 Two Balls Collide Two billiard balls of equal and known mass m are traveling with known velocities V 1 and V 2. They collide elastically What are the velocities after the collision?

31. Physics 218, Lecture XIV31 A Ball collides with a Stationary Ball We have two billiard balls of different and known masses m 1 and m 2. Ball one is traveling with known velocity V 1. They collide elastically What are the velocities after the collision?

32. Physics 218, Lecture XIV32 Collisions and Impulse

33. Physics 218, Lecture XIV33 Playing Pool: 2 Dimensions Before the collision, ball 1 moves with speed V 1 in the x direction, while ball 2 is at rest. Both have equal mass. After the collision, the balls go off at angles  and –  What are v’ 1 and v’ 2 after the collision?  