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Physics 218
Lecture 16
Dr. David Toback
Physics 218, Lecture XVI
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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
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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
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Chapter 10: Momentum
Want to deal with more
complicated systems
• Collisions
• Explosions
Newton’s laws still work, but
we need some new ideas
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Today’s 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
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Definition of Linear Momentum
Vector equation!


P  mV

Psystem

  miVi
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Restating Newton’s Second Law
“The rate of change of momentum of an object is equal to
the net force applied to it”

dP
dt

F 
Do a check for constant mass :

dP
dt


d ( mV )
dt
 m

d (V )
dt

 ma
If we exert a net force on a body, the momentum of the
body
changes
Physics
218,
Lecture XVI
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What if SF=0?
If SF=0, then dp/dt = 0,

p = constant
Momentum doesn’t change


mv  m' v '
momentum before = momentum after
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Conservation of Momentum
For a system, by Newton’s laws, SF=0
Conservation of Momentum

 miv i 
i

' '
 mi v i
i
Sum of all
Sum of all
momentum before = momentum after
True in X and Y directions separately!
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Problem Solving
For Conservation of Momentum problems:
1. BEFORE and AFTER
2. Do X and Y Separately
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Before
Y
X
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After
X
Y
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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?
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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
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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
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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?
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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?
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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
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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
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Energy and Momentum in Collisions
Definitions:
• Elastic collision = kinetic
energy is conserved
• Inelastic collision =
kinetic energy is not
conserved.
• Momentum conserved?
• Total Energy conserved?
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Inelastic Collisions
• By definition:
Inelastic =
mechanical energy not conserved =
kinetic energy not conserved
• Inelastic Example: Two trains
which collide and stick together
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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.
1. What is their speed after the collision?
2. Show that this is inelastic
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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?
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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
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Coming up…
• 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
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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
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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
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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?
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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
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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?
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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?
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Collisions and Impulse
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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
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