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Physics 218 Lecture 16

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Title: Physics 218 Lecture 16


1
Physics 218Lecture 16
  • Dr. David Toback

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

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

4
Chapter 10 Momentum
  • Want to deal with more complicated systems
  • Collisions
  • Explosions
  • Newtons laws still work, but we need some new
    ideas

5
(No Transcript)
6
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

7
Definition of Linear Momentum
  • Vector equation!

8
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

9
What if SF0?
  • If SF0, then dp/dt 0, ? p constant
  • Momentum doesnt change
  • momentum before momentum after

10
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!

11
Problem Solving
  • For Conservation of Momentum problems
  • BEFORE and AFTER
  • Do X and Y Separately

12
Before
Y
X
13
After
Y
X
14
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?

15
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

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

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?

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?

19
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

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.
  • 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

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?

22
Inelastic Collisions
  • By definition
  • Inelastic
  • mechanical energy not conserved
  • kinetic energy not conserved
  • Inelastic Example Two trains which collide and
    stick together

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

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?

25
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

26
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

27
End of Lecture Notes
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
  • 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

29
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

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?

31
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

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?

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?

34
Collisions and Impulse
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 v1 and v2
after the collision?
Q
-Q
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