1. Physics 218 Lecture 16
Dr. David Toback
Physics 218, Lecture XVI

2. Checklist for Today Things that were due Monday:
Chapter 8 Quizzes on WebCT
Things due today:
Read Chapters 10 & 11
Things that are due tomorrow in Recitation
Chapter 9 problems
Physics 218, Lecture XVI

3. The Schedule This Week: (3/17) Chapter 8 quizzes due in WebCT
Reading for Chapters 10 & 11
Lecture on Chapter 10 (11 in recitation)
Chapter 9 and Exam 2 Review in recitation
Next Week: (3/24)
Chapter 9 due in WebCT (mini-practice exam 2 available)
Exam 2 on Tuesday
Recitation on Chapters 10 & 11
Reading for Chapters 12 & 13 for Thursday
Lecture 12 & 13 on Thursday
Following week
Chapter 10 & 11 material in WebCT
Reading: Chapters 14-16
Lectures on (Lectures 1 and 2 of Four)
Recitation on Chapters 12 & 13
Physics 218, Lecture XVI

4. Chapter 10: Momentum Want to deal with more complicated systems
Collisions
Explosions
Newton’s laws still work, but we need some new ideas
Physics 218, Lecture XVI

5. Physics 218, Lecture XVI

6. Today’s Lecture Things colliding Things exploding
Different style than in the textbook
Begin with a definition of Linear Momentum
Then show that conservation of momentum helps us solve certain types of problems
Things colliding
Things exploding
Physics 218, Lecture XVI

7. Definition of Linear Momentum
Vector equation!
Physics 218, Lecture XVI

8. 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
Physics 218, Lecture XVI

9. Momentum doesn’t change momentum before = momentum after
What if SF=0?
If SF=0, then dp/dt = 0,  p = constant
Momentum doesn’t change
momentum before = momentum after
Physics 218, Lecture XVI

10. Conservation of Momentum
For a system, by Newton’s laws, SF=0
Conservation of Momentum
Sum of all Sum of all
momentum before = momentum after
True in X and Y directions separately!
Physics 218, Lecture XVI

11. Problem Solving BEFORE and AFTER Do X and Y Separately
For Conservation of Momentum problems:
BEFORE and AFTER
Do X and Y Separately
Physics 218, Lecture XVI

12. Before Y X
Physics 218, Lecture XVI

13. After Y X
Physics 218, Lecture XVI

14. 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?
Physics 218, Lecture XVI

15. 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
Physics 218, Lecture XVI

16. 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
Physics 218, Lecture XVI

17. Simple Gun Example
A gun of mass MG is sitting at rest with a bullet of mass MB inside it. You shoot the gun and the bullet comes out with a speed V at angle Q.
What is the recoil velocity of the gun?
Physics 218, Lecture XVI

18. 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?
Physics 218, Lecture XVI

19. SF=0, then dp/dt = 0, → p = constant
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?
SF=0, then dp/dt = 0, → p = constant
Physics 218, Lecture XVI

20. 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
Physics 218, Lecture XVI

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

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

23. Colliding Trains: 1 Dimension
The train car on the left, mass m1, is moving with speed Vo when it collides with a stationary car of mass m2. The two stick together.
What is their speed after the collision?
Show that this is inelastic
Physics 218, Lecture XVI

24. Ballistic Pendulum
A bullet of mass m and velocity Vo 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?
Physics 218, Lecture XVI

25. 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
Physics 218, Lecture XVI

26. Coming up… Mini-practice exam 2 and bonus points
Yesterday: Chapter 8 quizzes in WebCT if you haven’t finished them already
Tomorrow: Recitation on Chapter 9 and exam review
Next Lecture: Finish Chapter 10
Next week:
Homework 9 due
Mini-practice exam 2 and bonus points
Exam 2, Tuesday March 25th
Start Chapters 12-16
Physics 218, Lecture XVI

27. End of Lecture Notes
Physics 218, Lecture XVI

28. 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
Physics 218, Lecture XVI

29. Next time: Exam 1 material, Chapter 3(9)
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
Physics 218, Lecture XVI

30. Head On Collision
A ball of mass m1 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 m2?
Physics 218, Lecture XVI

31. 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
Physics 218, Lecture XVI

32. Two Balls Collide
Two billiard balls of equal and known mass m are traveling with known velocities V1 and V2. They collide elastically
What are the velocities after the collision?
Physics 218, Lecture XVI

33. A Ball collides with a Stationary Ball
We have two billiard balls of different and known masses m1 and m2. Ball one is traveling with known velocity V1. They collide elastically
What are the velocities after the collision?
Physics 218, Lecture XVI

34. Collisions and Impulse
Physics 218, Lecture XVI

35. Playing Pool: 2 Dimensions
Before the collision, ball 1 moves with speed V1 in the x direction, while ball 2 is at rest. Both have equal mass. After the collision, the balls go off at angles Q and –Q. What are v’1 and v’2 after the collision? Q -Q
Physics 218, Lecture XVI