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Unformatted text preview: u in any direction. The force of gravity that acts on the body is F =-( mMG/r 2 ) r , where M is the mass and R is the radius of the moon. Show that the body cannot escape from the moon if u 2 &lt; 2 MG/R . 5. The potential energy between two atoms in a molecule is U ( x ) =-a x 6 + b x 12 (2) where a and b are positive constants. Assume that one of the atoms is very heavy and remains at the origin at rest, and the other is much less massive and moves only in the x-direction. (a) Find the force F ( x ). Sketch U ( x ) and F ( x ) for the case a = b = 1. (b) Find the position of equilibrium and check stability. Give a numerical value for the equilibrium position for a = b = 1. (c) Find the period for small oscillations around the equilibrium position. 1...
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This note was uploaded on 09/20/2010 for the course AMATH 261 taught by Professor Rogermelko during the Spring '10 term at Waterloo.
- Spring '10