Chapter 8 Potential Energy and Conservation of Energy

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Chapter 8 - Potential Energy and Conservation of
Energy

• Conservative vs. Non-conservative Forces
• Definition of Potential Energy
• Conservation Of Mechanical Energy
• Determining Potential Energy
• Gravitational near the surface of the earth
• Gravitational anywhere - escape velocity
• Elastic
• Determining the Force From Potential Energy
  Functions
• Work Done by Non-conservative Forces
• Power

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Power

• Rate at which work is done.
• Average Power
• Instantaneous Power

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Units
Watt (W) J/s N-m/s
HP 550 ft-lb/s
Power
M-L2/T3
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Conservative vs. Non-conservative

• Conservative - A force is said to be conservative
  if the work done by the force acting on a object
  moving between two points is independent of the
  path the particle takes between the points.
• Non-conservative - depends on the path

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Example Gravity near the surface of the earth
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Alternative definition

• A force is conservative if the net work done by
  the force on an object moving around any closed
  path is zero.

Gravity is a conservative force!
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A nonconservative force
Friction is a nonconservative force!
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Potential Energy

• Energy associated with the position or
  configuration of a system.
• The change in potential energy associated with a
  particular conservative force is the negative of
  the work done by that force.

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Examples

• Gravity
• Springs

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Differential form
One dimension
Three dimensions
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Potential Energy Summary

• Potential energy is only associated with
  conservative forces. It is the negative of the
  work done by the conservative force.
• The zero point of potential energy is arbitrary
  and should be chosen where it is most
  convienient.
• Potential energy is not something a body has by
  itself, but rather is associated with the
  interaction of two or more objects.

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Conservation of Mechanical Energy
Work-Energy Principle
Definition of Potential Energy
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Problem solving strategy
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Who is going faster at the bottom?

• Assume no friction
• Assume both have the same speed pushing off at
  the top

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Problem 1

• A Block of mass m is released from rest and
  slides down a frictionless track of height h
  above a table. At the bottom of the track, where
  the surface is horizontal, the block strikes and
  sticks to a light spring.
• Find the maximum distance the spring is
  compressed.
• m 2 kg, h 1 m, k 490 N/m

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Problem 2

• A ball (mass m) on a string (length L) is
  released from rest with the string horizontal.
  What is the speed when it reaches its lowest
  point?
• What if the string was not horizontal, instead
  being released from some angle q?

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Energy conservation with dissipative forces

• Total energy is neither increased or decreased in
  any process. Energy can be transformed from one
  form to another, and transferred from one body to
  another, but the total amount remains constant.

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Example 3

• A roller coaster with mass of 1000 kg starts at a
  height of 40 m and is found to reach a height of
  only 25 m before coming to a stop. It traveled a
  distance of 400 m. Estimate the average friction
  force.
• Is the friction force constant?

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Problem 7

• A 2 kg block is attached to a light spring of
  force constant 500 N/m. The block is pulled 5 cm
  to the right and of equilibrium. How much work
  is required to move the block?
• If released from rest, find the speed of the
  block as it passes back through the equilibrium
  position if
• the horizontal surface is frictionless.
• the coefficient of friction is 0.35.

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Example

• A ball of mass 4.64 kg is taken to a position 3
  moon radii above the surface of the moon where it
  is dropped from rest. What is the speed of the
  ball as it just starts to make contact with the
  surface of the moon?
• Mm 7.35 x 1022 kg
• Rm 1.74 x 106 m

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Gravitational potential energy again
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Escape velocity