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Physics 1A, Section 2. November 1, 2010. Office Hours. Office hours will now be: Tuesday, 3:30 – 5:00 PM (half an hour later) still in Cahill 312. Today’s Agenda. Finish energy problem from Thursday forces and potential energy potential energy of a fictitious force?

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Physics 1a section 2

Physics 1A,Section 2

November 1, 2010


Office hours
Office Hours

  • Office hours will now be:

    • Tuesday, 3:30 – 5:00 PM (half an hour later)

    • still in Cahill 312


Today s agenda
Today’s Agenda

  • Finish energy problem from Thursday

  • forces and potential energy

  • potential energy of a fictitious force?

  • potential energy applied to orbits

    • Lagrange points for Sun/Earth/satellite



Quiz problem 501
Quiz Problem 50

  • Answer:

  • v = sqrt(2gh)

  • F = -kx – mmg, to the right

  • W = -kxs2/2 – mmgxs

  • Wf = 2mmgxs

  • h’ = h – 2mxs

  • xs = [-mmg + sqrt(m2m2g2+2kmgh)]/k


Conservative and non conservative forces
Conservative andNon-Conservative Forces

  • A conservative force F can be associated with a potential energy U

    • F = –dU/dr or –dU/dx in Physics 1a

      • F = (–U/x, –U/y, –U/z) more generally

    • Force is a function of position only.

    • example: uniform gravity: U = mgz

    • example: Newtonian gravity: U = –GMm/r

    • example: ideal spring: U = kx2/2

  • Non-conservative forces

    • friction: force depends on direction of motion

    • normal force: depends on other forces

      • but does no work because it has no component in direction of motion.


Potential energy from a fictitious inertial force
Potential Energy from a Fictitious (Inertial) Force

  • It can be useful to associate the centrifugal force in a rotating frame with a potential energy:

    • Fcentrifugal = mw2r (outward)


Potential energy from a fictitious inertial force1
Potential Energy from a Fictitious (Inertial) Force

  • It can be useful to associate the centrifugal force in a rotating frame with a potential energy:

    • Fcentrifugal = mw2r (outward)

    •  Ucentrifugal = –mw2r2/2


Consider circular orbits again
Consider circular orbits (again)

  • Work in the rotating (non-inertial) frame.

  • planet orbiting the Sun:

    • Utotal = Ugravity + Ucentrifugal

    • Equilibrium where dUtotal/dr = 0  GMSun = w2r3


Consider circular orbits again1
Consider circular orbits (again)

  • Work in the rotating (non-inertial) frame.

  • planet orbiting the Sun (Mplanet << Msun):

    • Utotal = Ugravity + Ucentrifugal

    • Equilibrium where dUtotal/dr = 0  GMSun = w2r3

  • Satellite and Earth orbiting the Sun (Msatellite << MEarth << MSun)

    • Utotal = Ugravity,Sun + Ugravity,Earth + Ucentrifugal

    • Equilibria at 5 Lagrange points


Sun earth lagrange points
Sun-Earth Lagrange Points

image from wikipedia


Location of lagrange points
Location of Lagrange points

  • L1,L2: DR ≈ R(ME/3MS)1/3

    • about 0.01 A.U. from Earth toward or away from Sun

    • unstable equilibria

  • L3: orbital radius ≈ R[1 + (5ME/12Ms)]

    • very unstable equilibrium

  • L4,L5: three bodies form an equilateral triangle

    • stable equilibria (via Coriolis force)

1 A.U. = astronomical unit = distance from Earth to Sun




Thursday november 4
Thursday, November 4:

  • Quiz Problem 38 (collision)

  • Optional, but helpful, to try this in advance.


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