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Physics 218Lecture 16

- Dr. David Toback

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

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 14-16 (Lectures 1 and 2 of Four)
- Recitation on Chapters 12 13

Chapter 10 Momentum

- Want to deal with more complicated systems
- Collisions
- Explosions
- Newtons laws still work, but we need some new

ideas

(No Transcript)

Todays Lecture

- 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

Definition of Linear Momentum

- Vector equation!

Restating Newtons 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

What if SF0?

- If SF0, then dp/dt 0, ? p constant
- Momentum doesnt change
- momentum before momentum after

Conservation of Momentum

- For a system, by Newtons laws, SF0
- Conservation of Momentum
- Sum of all Sum of

all - momentum before momentum after
- True in X and Y directions separately!

Problem Solving

- For Conservation of Momentum problems
- BEFORE and AFTER
- Do X and Y Separately

Before

Y

X

After

Y

X

So what?

- Momentum is useful when we dont 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?

Everyday Experience?

- Question Why do you go backwards when you push

someone on the ice? - Newtons Laws answer When you exert a force on

another person, then, by Newtons law, the person

exerts an equal and opposite force on you

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

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?

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?

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?
- SF0, then dp/dt 0, ? p constant

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. - Newtons Law For every action there is an equal

and opposite reaction - Add up all the momentums in the problem
- The forcer and the forcee

Energy and Momentum in Collisions

- Definitions
- Elastic collision kinetic energy is conserved
- Inelastic collision kinetic energy is not

conserved. - Momentum conserved?
- Total Energy conserved?

Inelastic Collisions

- By definition
- Inelastic
- mechanical energy not conserved
- kinetic energy not conserved
- Inelastic Example Two trains which collide and

stick together

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

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?

Bottom line When to use Momentum

- When you dont 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

Coming up

- Yesterday Chapter 8 quizzes in WebCT if you

havent 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

End of Lecture Notes

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
- Todays 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

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 Ill grant an

extension. Questions 1 14

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?

Next time

- Exam Thursday
- Extra credit if you have 100s on all HWs, HW

quizzes and math quizzes before the exam - Reading for Tuesday
- Rest of Chapter 9 on Momentum

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?

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?

Collisions and Impulse

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 v1 and v2

after the collision?

Q

-Q