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Physics 218 Lecture 16 Dr. David Toback – PowerPoint PPT presentation

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Title: Physics%20218%20Lecture%2016

1
Physics 218 Lecture 16
• Dr. David Toback

2
Checklist for Today
• Things that were due Monday
• Chapter 8 Quizzes on WebCT
• Things due today
• 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
• 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
• 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?
• 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
• 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.
• Rest of Chapter 9 on Momentum
• Reading was due today, but Ill grant an
extension. Questions 1 14

30
• 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
• 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