Physics 2211a Kulp Class 29: What is a perfectly elastic collision

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Physics 2211a (Kulp)Class 29 What is a
perfectly elastic collision?

• W. D. Kulp
• william.kulp at physics.gatech.edu
• Office W501b
• Office Hours MF 11-12 AM, Tu 9-10 AM, by appt.
• www.physics.gatech.edu/academics/Classes/fall200
  6/2211/a/

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Where were we?

• Last class Class 28

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• A 20-cm-tall spring with spring constant 5000 N/m
  is placed vertically on the ground. A 10.2 kg
  block is held 15 cm above the spring. The block
  is dropped, hits the spring, and compresses it.
  What is the height of the spring at the point of
  maximum compression?

• H 20 yf
• (Note that yf lt 0)

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• A 20-cm-tall spring with spring constant 5000 N/m
  is placed vertically on the ground. A 10.2 kg
  block is held 15 cm above the spring. The block
  is dropped, hits the spring, and compresses it.
  What is the height of the spring at the point of
  maximum compression?

ye
6 cm
-10 cm

• H 20 - 10 10 cm

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Where are we?

• Last class Class 28 (springs)

• Today Class 29
• Analyze a perfectly elastic collision using
  conservation of linear momentum and conservation
  of energy.
• Interpret an energy diagram to analyze the motion
  of a particle.

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Elastic collisions

• Consider an elastic collision between two
  particles where one particle is initially at rest.

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2

• It can be shown (in the textbook) that the final
  velocities are simply related to the initial
  velocity of m1

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Elastic collisions

• Some limiting cases to consider

m1 m2
0
v1ix
2v1ix
v1ix
0
-v1ix

• What happens when both particles are moving
  initially?

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Elastic collisions

• If both particles have an initial velocity, use a
  Galilean transformation to analyze the collision
  in a frame where one particle is initially at
  rest.

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Newtons Cradle

• conservation of energy and momentum are
  satisfied
• energy is stored in minute compression of
  billiard balls
• for a ball in the middle, the net impulse is
  zero
• net impulse is not zero for a ball at the end
• What happens when more than one ball is pulled
  back?

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Graphs of potential energy

• Consider a particle with total energy of E 1.5
  J.
• Where does it speed up?
• Where does it slow down?
• Where are the turning points in the motion?

• Speeds up approaching x 1 and x 3.
• Slows down departing x 1 and x 3.
• Turns around when U Etot x 0 and x 4.

What energy transformations take place?
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Graphs of potential energy

• Consider a particle with total energy of E 1.0
  J.
• Where does it speed up?
• Where does it slow down?
• Where are the turning points in the motion?

• Speeds up approaching x 1 and x 3.
• Slows down departing x 1 and x 3.
• Turns around when U Etot x 0 and x 4 or
  approaching x 2.

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Graphs of potential energy

• Consider a particle with total energy of E 2.5
  J.
• Where does it speed up?
• Where does it slow down?
• Where are the turning points in the motion?

• Speeds up approaching x 1 and x 3
• Slows down departing x 1 and x 3
• Turns around approaching x 0 only
• Motion is constant right of x 4

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Graphs of potential energy

• Consider a particle with total energy of E 1.5
  J that is moving to the left. Just as it passes
  x 2 m, it collides with another particle. The
  collision increases the particles energy by 1.0
  J. What happens to it?

• The particle speeds up or slows down as before
  the collision.
• The turning points change after the collision.
  The particle still rebounds approaching x 0,
  but now can escape at x 4.
• A model of photodissociation, or a nuclear
  reaction.

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Whats next?

• Wednesday, 11/1 Class 30 How is energy
  transferred?
• Calculate analytically or graphically the work
  done on an object.
• Determine the change in kinetic energy or motion
  that results from performing an amount of work
  on an object.
• Use the scalar (dot) product operation to
  calculate the work done on an object.
• Given an object with a change in speed or kinetic
  energy, calculate the work performed by the net
  force (or by each of the component forces).
• Apply the work-energy theorem to determine the
  change in an objects kinetic energy and analyze
  the motion of the object.

• To-do list
• Homework 28 before class on Wednesday
• Read assignment (11.1 - 11.4)

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Parallel springs

• Consider two massless springs connected in
  parallel. The springs (spring constants k1 and
  k2) are connected via a thin, vertical rod. A
  constant force, F, is exerted on the rod. The
  springs are extended by the same amount.
• This system of two springs is equivalent to a
  single spring, of spring constant k, where k is
  equal to

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A perfectly elastic collision is

• a collision between two springs.
• a collision that conserves thermal energy.
• a collision that conserves kinetic energy.
• a collision that conserves potential energy.
• a collision that conserves mechanical energy.

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• The momentum of the ball moving in frame S is

• less than it is in frame S.
• the same as in frame S.
• greater than in frame S.