Collisions ??

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Collisions??
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A collision is an interaction involving large
forces acting for a short time.
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During the short time of the collision, internal
forces are much bigger than external forces. We
can ignore the external forces during the
collision.
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Momentum principle
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Energy principle
(Careful total energy is conserved, but the
kinetic energy might not be conserved! Some might
be converted to heat.)
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We might still need to account for external
forces during the time before and after the
collision. Example Gravity, acting on these two
balls, is important before and after they
collide. But during the collision, we can ignore
it.
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Elastic collisions ????

• If the internal energy of the objects does not
  change
• No change in temperature
• No change in shape
• No springs compressed
• No new rotations or vibrations
• Then

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Elastic collision of equal masses
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Inelastic collisions ?????

• If the internal energy of the objects does
  change
• Change in temperature
• Change in shape
• Springs compressed, or
• New rotations or vibrations
• Then

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Maximally inelastic collision (sticking
collision) of equal masses
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How much kinetic energy was lost?
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Head-on collision of unequal masses
System Ping-pong ball bowling
ball Surroundings Nothing significant.
Initial state Ping-pong ball moving, bowling
ball at rest. Final state Ping-pong ball
bounces back with almost unchanged speed
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Head-on collision of unequal masses
Momentum principle
The bowling ball ends up with about twice the
momentum of the Ping-pong ball! How fast does it
move?
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Head-on collision of unequal masses
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40 m/s
EARTH
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What is the recoil speed of the Earth?
??
40 m/s
v ?
EARTH
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40 m/s
v ?
At this speed, it would take over one million
years to move the width of a single atom!
EARTH
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Collisions in 2-D and 3-D
Momentum
x
Initial
y
Final
Energy (elastic collision)
y
x
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Collisions in 2-D and 3-D

• Three equations
• Four unknowns!
• p3
• p4
• ?
• f
• These equations are only useful if we can somehow
  measure at least one of the unknowns.

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In particle physics experiments, the momentum of
a particle is measured by how much it curves in a
magnetic field.
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Special case Identical particles, one at rest.
Momentum
Initial
Energy (elastic collision) (for v ltlt c)
Final
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Special case Identical particles, one at rest.
Momentum
Initial
Energy (elastic collision)
Final
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Special case Identical particles, one at rest.
Momentum
Initial
Energy (elastic collision)
Final
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Special case Identical particles, one at rest.
Momentum
Initial
Energy (elastic collision)
Final
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How the nucleus was discovered by collisions
Born in 1871, the son of a poor farmer in New
Zealand. Won the Nobel prize (chemistry) in
1908. Died in 1937, in Cambridge, as Lord
Rutherford of Nelson.
Ernest Rutherford
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Thompsons plum pudding model for the atom
In 1909, Rutherford decided to test this model by
shooting alpha particles (helium nuclei) at a
thin sheet of gold. At this stage, he had
already won his Nobel prize for other work.
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The experiment
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What should have happened
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What actually happened
Rutherford thought he was shooting bowling balls
at ping-pong balls. Actually, he was shooting
bowling balls at even bigger bowling balls.
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It was the most incredible event that has ever
happened to me in my life. It was almost as
incredible as if you fired a 15 inch shell (??)
at a piece of tissue paper and it came back and
hit you.