Physics 101: Lecture 12 Collisions and Explosions

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Physics 101 Lecture 12Collisions and Explosions

• Todays lecture will cover Textbook Sections 7.5
  - 7.8

Quiz this week Relative velocity, friction,
circular motion
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Overview of Semester

• Newtons Laws
• S F m a
• Work, Kinetic Energy, Potential Energy
• S Wnc DK DU Energy is conserved
• Impulse-Momentum
• S F m a multiply both sides by Dt
• S I Dp Momentum is conserved
• Works in each direction independently

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Collisions
Procedure

• Draw before, after
• Include all participating bodies (Fext 0)
• Set up axes
• Compute Ptotal before
• Compute Ptotal after
• Set them equal to each other
• Solve

Explosions
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ACT

• 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?
• A. V
• B. V/2
• C. V/4
• D. 0

S Pinitial S Pfinal M V M Vf M Vf V
2Vf Vf V/2
Demo with gliders
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ACT

• What physical quantities are conserved in the
  previous collision?
• A. Only momentum is conserved B. Only total
  mechanical energy is conserved C. Both are
  conserved D. Neither is conserved

Mechanical Energy Kinetic Energy Potential E
½ m v2 0 Kinitial ½ m v2
Kfinal ½ m (v/2)2 ½ m (v/2)2 ¼ m v2
HEAT or work on bodies
Where did the energy go?!

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

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Preflight 1 2

• 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

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Objects with a completely inelastic collision
and don't move after the collision will have zero
total momentum and kinetic energy. For example, a
car crash that is a head on collision with cars
that are traveling at the same speed with the
same weight would not have any momentum or
kinetic energy after the crash.
glider demo
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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 0m v (Mm) V
After, Conserve Energy ½ (Mm) V20 0(Mm) g
H V ?(2gH)
demo
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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 speed?
• 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!!

0 p1p2 p1 -p2
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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
SPx 0, but SPy gt 0
SPx 0, and SPy 0
Which of these is possible? (Ignore friction and
gravity) A. A B. B C. Both D. Neither
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Shooting Pool...
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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...

• pi p1 p2
• pi2 p12 p22 2p1p2cos(q)
• pi2/2m (p12/2m p22/2m) 2p1p2cos(q)
• 0 2p1p2cos(q)
• cos(q)0
• q 90o
• Then the angle between the balls after the
  collision is 90o

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Shooting Pool...

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

demo
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Center of Mass

• Shown is a yummy doughnut. Where would you
  expect the center of mass of this breakfast of
  champions to be located?

The center of mass of any ring is at the center
of the ring (in the air). The donut is a ring
and therefore, the center of mass should be
exactly in the center.
It would most likely be inside of my stomach
somewhere absorbing all of the vodka, but before
I ate it it would be in the middle hole of the
donut.
I would expect it to be on the edge of the
doughnut
it will be distributed throughout the dounut
since there is no center
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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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Center of Mass
Ptot MtotVcm
FextDt DPtot MtotDVcm
So if 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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