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Physics 1A - Understanding Potential Energy and Orbits

Learn about potential energy, forces, orbits, Lagrange points, and more in Physics 1A. Dive into concepts like conservative vs. non-conservative forces and the role of fictitious forces in calculating potential energy.

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Physics 1A - Understanding Potential Energy and Orbits

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  1. Physics 1A,Section 2 November 1, 2010

  2. Office Hours • Office hours will now be: • Tuesday, 3:30 – 5:00 PM (half an hour later) • still in Cahill 312

  3. 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

  4. Quiz Problem 50

  5. 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

  6. 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.

  7. 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)

  8. 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

  9. 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

  10. 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

  11. Sun-Earth Lagrange Points image from wikipedia

  12. 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

  13. Advanced Composition Explorer – examines solar wind

  14. Planck satellite – examines relic radiation from Big Bang

  15. Thursday, November 4: • Quiz Problem 38 (collision) • Optional, but helpful, to try this in advance.

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