Physic 110 Lecture 16 from Chapter 6'''Section 2

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Physic 110 Lecture 16 from Chapter
6...Section 2

• Conservation of Momentum

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Questions on Assignment 15?

• Assignment
• Conceptual Question
• Chapter 6, C.Q. 13 on page 181 Chapter 6,
  C.Q. 16 on page 181
• Problems
• Chapter 6, Problem 1 on page 181
• Chapter 6, Problem 10 on page 182 Chapter
  6, Problem 12 on page 182

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Homework assignment 16

• Assignment
• Conceptual Question
• Chapter 6, C.Q. 5 on page 181
• Problems
• Chapter 6, Problem 19 on page 183
• Chapter 6, Problem 24 on page 183
• Chapter 6, Problem 27 on page 183

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Momentum

• where m is mass
• v is velocity

Impulse
where F is average contact force ?t
is time of contact
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Impulse-Momentum Theorem

• An impulse acting on a system causes a change in
  the systems momentum.

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Example 1

• A 0.05kg golf ball is struck by a club with an
  average force of 2 kN for 1 ms.
• What speed does the ball leave the tee with?

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Example 1

• m 0.05kg
• F 2 kN 2000 N
• ?t 1ms 0.001s
• Vi 0 m/s

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Conservation of Momentum

• If no external force or impulse acts on a system,
  then the systems momentum is conserved.
• A system may consist of several bodies which all
  have individual momentum.

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Example 2

• A 75 kg man stands in the middle of frozen lake
  (assume circular with diameter of 100 m). He
  cannot move because the ice is frictionless. He
  luckily is holding a 1.5 kg physics textbook.
  He tosses the book horizontally at 5.0 m/s.
• Does the man move and why?
• How long will it be before the book reaches
  shore?
• How long will it be before the man reaches shore?
• Should he how far will he have to walk to go get
  the physics book?

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Example 2

• At the start, there is no motion, so the total
  momentum is 0.
• If he throws the book away from him, in order for
  the momentum to remain zero, he must start moving
  in the opposite direction.

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Example 2

• vbook -5.0 m/s mbook1.5 kg
• vman ? mman 75 kg

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Example 2

• vbook -5.0 m/s mbook1.5 kg
• vman ? mman 75 kg

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Example 2

• How long to reach shore? (50 m away)
• Book Man

x
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Collisions

• The conservation of momentum applies even when
  bodies collide with each other.
• Momentum is exchanged between colliding objects,
  but the total momentum of all objects combined
  must remain constant.

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Different object momentums, but same total
momentum
After collision
Before collision
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Conservation of Momentum for system of objects

• Momentum is conserved for the system of objects
• The system includes all the objects interacting
  with each other
• Assumes only internal forces are acting during
  the collision
• Can be generalized to any number of objects

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Types of Collisions

• Inelastic collisions
• Kinetic energy is not conserved
• Some of the kinetic energy is converted into
  other types of energy such as heat, sound, work
  to permanently deform an object
• Perfectly inelastic collisions occur when the
  objects stick together
• Even then not all of the KE is necessarily lost

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Example 3

• A 75 kg ice skater moving at 10 m/s crashes into
  a stationary skater of equal mass. They grab a
  hold of each other and move off after the
  collision together. How fast do they travel
  following the collision?

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Example 3

• A 75 kg ice skater moving at 10 m/s crashes into
  a stationary skater of equal mass. They grab a
  hold of each other and move off after the
  collision together. How fast do they travel
  following the collision?

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Example 3

• Conservation of momentum before and after the
  collision

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Example 3

• Conservation of momentum before and after the
  collision

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Inelastic Collisions Summary

• When two objects stick together after the
  collision, they have undergone a perfectly
  inelastic collision
• Conservation of momentum becomes