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Title: -Gravitational Field -Gravitational Potential Energy


1
-Gravitational Field-Gravitational Potential
Energy
  • AP Physics C
  • Mrs. Coyle

2
Remember Newtons Law of Universal Gravitation
-Universal Gravitation Constant G6.67x 10-11
Nm2/kg2 -The gravitational force is a field
force.
3
Review Question
  • Which exerts a greater force, the earth on the
    moon or the moon on the earth?

4
  • Gravitational Field the space around a mass.
    Here a test mass would feel a gravitational
    force.
  • Gravitational Field Vector

5
Gravitational Field Vector, g at the surface of
the Earth
6
g above the Earths surface
  • r RE h
  • Note
  • g decreases with increasing altitude
  • As r ?, the weight of the object approaches
    zero

7
Variation of g with Height from the surface of
the Earth
8
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

9
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

10
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.

11
Gravitational Potential Energy
  • As a particle moves from A to B, its
    gravitational potential energy changes by

12
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

13
Gravitational Potential Energy of the
Earth-particle system
14
Gravitational Potential Energy of any two
particles
15
Gravitational Potential Energy of a system of any
two particles
  • U -Gm1m2
  • r
  • The reference point U0
  • is at infinity.

16
Gravitational Potential Energy
17
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).

18
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.

19
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

20
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.

21
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.

22
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
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