a2 - u in any direction. The force of gravity that acts on...

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Phys 263/Amath 261 Assignment 2 Due: Monday, May 26, 2008 (in class) 1. The “Law of conservation of mass” states that the mass of a closed system (i.e. with no outside influence) will remain constant. Why is this only an approximate conservation law? Name two cases where it breaks down. 2. The motor of a speed boat is shut off when it has attained a speed of v 0 , at t = 0. Starting from t = 0, the boat is slowed down by a retarding force F = Ce - kv . Calculate v ( t ) and x ( t ). How long will it take for the boat to stop, and how much distance will it travel before stopping? 3. Find the displacement as a function of time for an electron in the upper atmosphere, which experiences a time dependent force due to the presence of radio waves. The force is given by: F ( t ) = - eE 0 sin( ωt ) (1) where e is the charge on an electron and E 0 sin( ωt ) is the electric field of the radio waves. 4. A body of mass m is projected from the surface of the moon with a speed
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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 < 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.

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