DQ1C_solution - Discussion Question 1C P212 Week 1 Review...

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Discussion Question 1C P212, Week 1 Review: Potential Energy 1 Four particles of equal mass M are fixed at the corners of a square with sides of length a . A fifth particle has mass m and moves under the gravitational forces of the other four. Consider the gravitational potential energy U of the mass m as a function of its position ( x , y ). This potential energy map U ( x , y ) is an extremely useful way of representing the effect of the gravitational force on the mass m : If m is held at rest at some point ( x 1 , y 1 ) and you let it go, it will always move toward a point of lower potential energy. You can therefore think of the function U ( x , y ) as a topographical map: the particle m will always “roll downhill” . If the mass m moves from point ( x 1 , y 1 ) to point ( x 2 , y 2 ), the potential energy difference U ( x 1 , y 1 ) – U ( x 2 , y 2 ) tells you exactly how much work was done by gravity, and exactly how much kinetic energy the particle gained as a result. Let’s visualize all this. The figures below show the potential energy map U ( x , y ) for the square configuration of four masses M illustrated above. The height of the surfaces indicates the magnitude of U at each point. Which one is correct?
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This note was uploaded on 06/16/2011 for the course PHYS 212 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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DQ1C_solution - Discussion Question 1C P212 Week 1 Review...

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