CPI: Lecture 12 Collisions and Explosions

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CPI Lecture 12Collisions and Explosions

• Todays lecture will cover Textbook Sections 7.4
  - 7

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Impulse and Momentumquick review of last lecture

• Momentum-Impulse Theorem
• Fave?t ? I pf - pi ?p
• For single object.
• If F 0, then momentum conserved (?p 0)
• For system of objects
• Ptotal ? ?p
• Internal forces forces between objects in
  system
• External forces all other forces
• Fext?t ?Ptotal
• if Fext 0 , then total momentum conserved
  (?Ptotal 0)
• Applications Collisions Explosions

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Collisions
Procedure

• Draw before, after
• Define system so that Fext 0
• Set up axes
• Compute Ptotal before
• Compute Ptotal after
• Set them equal to each other

Explosions
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Preflight 1

• A railroad car is coasting along a horizontal
  track with speed V when it runs into and connects
  with a second identical railroad car, initially
  at rest. Assuming there is no friction between
  the cars and the rails, what is the speed of the
  two coupled cars after the collision?
• 1. V
• 2. V/2
• 3. V/4
• 4. 0

S Pinitial S Pfinal M V M Vf M Vf V
2Vf Vf V/2
Demo with gliders
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Preflight 2 3

• What physical quantities are conserved in the
  above collision?
• 1. Only momentum is conserved 2. Only total
  mechanical energy is conserved 3. Both are
  conserved 4. Neither are conserved

Both momentum and mechanical energy are conserved
because there are no non conservative forces like
air resistance or friction.
once again....everything is conserved in
physicsland
There is always conservation momentum, and when
two thing collide each one's velocity changes,
because this is not an elastic case As for
mechanical energy, you know that energy is always
conserved, but there are more than 1 types of
energy and when it is conserved you must consider
all forms not just mechanical energy.
Mechanical Energy Kinetic Energy ½ m
v2 Kinitial ½ m v2 Kfinal ½ m
(v/2)2 ½ m (v/2)2 ¼ m v2
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Preflight 4 5

• Is it possible for a system of two objects to
  have zero total momentum and zero total kinetic
  energy after colliding, if both objects were
  moving before the collision?
• 1. YES
• 2. NO

if both objects are moving in opposite directions
with the same mass and velocity they would have a
resulting velocity of zero.
i really just dont think it is possible. but if i
am wrong, i am sure you will have a great demo to
make me feel dumb for answering the wrong
question.
Demo with gliders
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Some Terminology

• Elastic Collisions collisions that conserve
  energy
• Inelastic Collisions collisions that do not
  conserve energy
• Completely Inelastic Collisons objects stick
  together

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Ballistic Pendulum
L
L
V0
L
L
H
m
v
M m
V
M
A projectile of mass m moving horizontally with
speed v strikes a stationary mass M suspended by
strings of length L. Subsequently, m M rise
to a height of H.
Given H, M and m what is the initial speed v of
the projectile?
Collision Conserves Momentum m v (Mm) V
After, Conserve Energy ½ (Mm) V2 (Mm) g H V
sqrt(2 g H)
demo
See I.E. 1 in homework
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Explosions
v1
v2

• Example m1 M/3 m2 2M/3
• Which block has larger momentum?
• Each has same momentum
• Which block has larger velocity?
• mv same for each ? smaller mass has larger
  velocity
• Which block has larger kinetic energy?
• KE mv2/2 m2v2/2m p2/2m
• ? smaller mass has larger KE
• Is mechanical (kinetic) energy conserved?
• NO!!

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Collisions or Explosions in Two Dimensions

• Ptotal,x and Ptotal,y independently conserved
• Ptotal,x,before Ptotal,x,after
• Ptotal,y,before Ptotal,y,after

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Explosions ACT
before
Px 0 and Py 0
after
A
B
Px 0, but Py gt 0
Px 0, and Py 0
Which of these is possible? A B both
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Shooting Pool...

• Assuming
• Collision is elastic (KE is conserved)
• Balls have the same mass
• One ball starts out at rest
• Then the angle between the balls after the
  collision is 90o

pf
pi
vcm
Pf
F
before
after
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Shooting Pool...

• Tip If you shoot a ball spotted on the dot,
  you have a good chance of scratching !

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Center of Mass
Example 1
xCM (0 mL)/2m L/2
Example 2
xCM (0 5mL)/6m 5L/6
X0
XL
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Center of Mass (Preflight 6)

• Shown is a yummy doughnut. Where would you
  expect the center of mass of this breakfast of
  champions to be located? (Explain your reasoning
  Homer).

Well, I'm not really sure. If it were, say, a
cream filled donut (that has no hole), I would
expect the center of mass to be directly in the
middle. Since this donut has a hole in it's
middle, I'm baffled!
Dunkin Donuts cut it out and sold to 2nd graders
in the form of Munchkins! Mmm... munchkins.
They're almost as delicious and habit forming as
those chocolate cookies you hand out in class!!
I would expect the center of mass to be exactly
in the center of the hole. The center of mass
does not need to be inside the object, such as in
a boomerang, in which it is located outside of
the object.
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Center of Mass
Ptot MtotVcm
FextDt DPtot MtotDVcm
So is Fext 0 then Vcm is constant
Also Fext Mtotacm
Center of Mass of a system behaves in a SIMPLE
way- moves like a point particle!- velocity of
CM is unaffected by collision if Fext 0 (pork
chop demo)
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Summary

• Collisions and Explosions
• Draw before, after
• Define system so that Fext 0
• Set up axes
• Compute Ptotal before
• Compute Ptotal after
• Set them equal to each other
• Center of Mass (Balance Point)

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