Physics 2211: Lecture 37

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Physics 2211 Lecture 37
Elastic Collisions
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Types of Collisions
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ALL collisions obey the law of conservation of
momentum
An ELASTIC collision also obeys the law of
conservation of energy
For contact-type collisions, this amounts to
conservation of KE
An INELASTIC collision conserves momentum but not
KE.
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Billiards Collisions in Two Dimensions
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(No Transcript)
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Limits!
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Application do try this at home!
M gt gt m
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Application do try this at home!

• Find the rebound height
• of the small ball.
• H B) 2h C) 3h
• D) 4h E) 9h

M gt gt m
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m
M
Change to frame of reference where M is at rest
Change back to original frame
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Application balls of steel
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Momentum Conservation

• Two balls of equal mass are thrown horizontally
  with the same initial velocity. They hit
  identical stationary boxes resting on a
  frictionless horizontal surface.
• The ball hitting box 1 bounces back, while the
  ball hitting box 2 gets stuck.
• Which box ends up moving faster?

(1) Box 1 (2) Box 2 (3)
same
2
1
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Momentum Conservation

• Since the total external force in the x-direction
  is zero, momentum is conserved along the x-axis.
• In both cases the initial momentum is the same
  (mv of ball).
• In case 1 the ball has negative momentum after
  the collision, hence the box must have more
  positive momentum if the total is to be
  conserved.
• The speed of the box in case 1 is biggest!

x
V1
V2
2
1
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Momentum Conservation
mvinit (Mm)V2
mvinit MV1 - mvfin
V2 mvinit / (Mm)
V1 (mvinit mvfin) / M
x
V1
V2
2
1
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Explosion (inelastic un-collision)
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Explosion...

• No external forces, so P is conserved.
• Initially P 0
• Finally P m1v1 m2v2 0
• m1v1 - m2v2

M
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Comment on Energy Conservation

• We have seen that the total kinetic energy of a
  system undergoing an inelastic collision is not
  conserved.
• Energy is lost
• Heat (bomb)
• Bending of metal (crashing cars)
• Mechanical energy is not conserved since
  nonconservative work is done during the
  collision!
• Momentum along a certain direction is conserved
  when there are no external forces acting in this
  direction.
• In general, momentum conservation is easier to
  satisfy than energy conservation.

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Recap of todays lecture

• 1-D collisions elastic and inelastic
• Examples

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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, what is the initial speed v of the
projectile?
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Ballistic Pendulum...

• Two stage process

1. m collides with M, inelastically. Both M and
m then move together with a velocity V (before
having risen significantly).
2. M and m rise a height H, conserving KU
energy E. (no non-conservative forces acting
after collision)
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Ballistic Pendulum...

• Stage 1 Momentum is conserved

in x-direction

• Stage 2 KU Energy is conserved

Eliminating V gives
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Ballistic Pendulum
L
L
L
L
H
m
v
M m
M
d

• If we measure forward displacement d, not H

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Ballistic Pendulum
for
for d ltlt L
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Recap
Elastic Collisions
Next Lecture
Energy Diagrams