-Gravitational Field -Gravitational Potential Energy

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-Gravitational Field-Gravitational Potential
Energy

• AP Physics C
• Mrs. Coyle

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Remember Newtons Law of Universal Gravitation
-Universal Gravitation Constant G6.67x 10-11
Nm2/kg2 -The gravitational force is a field
force.
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Review Question

• Which exerts a greater force, the earth on the
  moon or the moon on the earth?

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• Gravitational Field the space around a mass.
  Here a test mass would feel a gravitational
  force.
• Gravitational Field Vector

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Gravitational Field Vector, g at the surface of
the Earth
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g above the Earths surface

• r RE h
• Note
• g decreases with increasing altitude
• As r ?, the weight of the object approaches
  zero

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Variation of g with Height from the surface of
the Earth
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Remember

• The gravitational force is conservative
• The gravitational force is a central force
• (A central force has a direction towards the
  center and its magnitude depends only on r)
• A central force can be represented by

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Work done by the Gravitational Force

• A particle moves from A to B while acted on by a
  central force F
• We approximate the path along A to B with radial
  and arc zigzags
• The work done by F along the arcs is zero
• The work done by F along the radial direction is

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Work done by the Gravitational Force

• The work done is independent of the path and
  depends only on rf and ri
• This proves that the gravitational force is
  conservative.

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Gravitational Potential Energy

• As a particle moves from A to B, its
  gravitational potential energy changes by

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Gravitational Potential Energy of the
Earth-particle system

• The reference point is chosen at infinity where
  the force on a particle would approach zero. Ui
  0 for ri
• 8This is valid only for r gt RE and not valid
  for r lt RE
• U is negative because of the choice of Ui

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Gravitational Potential Energy of the
Earth-particle system
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Gravitational Potential Energy of any two
particles
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Gravitational Potential Energy of a system of any
two particles

• U -Gm1m2
• r
• The reference point U0
• is at infinity.

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Gravitational Potential Energy
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Gravitational Potential Energy

• An outside force must do positive work to
  increase the separation between two objects
• This work gives the objects a greater potential
  energy (less negative).

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Binding Energy

• The absolute value of the potential energy is the
  binding energy
• An outside force must supply energy gretaer or
  equal to the binding energy to separate the
  particles to an infinite distance of separation.
• The excess energy will be in the form of kinetic
  energy of the particles when they are at infinite
  separation.

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Systems with Three or More Particles
(Configuration of Masses)

• The total gravitational potential energy of the
  system is the sum over all pairs of particles
• Gravitational potential energy obeys the
  superposition principle

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Systems with Three Particles

• The absolute value of Utotal represents the work
  needed to separate the particles by an infinite
  distance.
• Remember energy is a scalar quantity.

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Configurations of Masses

• Gravitational Forces are added using the vector
  component method.
• To find the Gravitational Potential Energy
• of the configuration of masses, the individual
  energies are added as scalars.
• A force would have to supply an amount of energy
  equal to the individual energy in order to
  separate the masses by an infinite distance.

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Ex 31

• A system consists of three particles, each of
  mass 5.00g, located at the corners of an
  equilateral triangle with sides of 30.0cm.
• Calculate the potential energy of the system.
• If the particles are released simultaneously,
  where will they collide?
• Ans a) -1.67x10-14 J