ENG102_SL3

ENG102_SL3 - DATE: October 9, 2011 DUE: October 14, 2011...

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Unformatted text preview: DATE: October 9, 2011 DUE: October 14, 2011 ENG102, Solution to homework set #3. 1. Look at Problem 3/101 in the book. a. Solve the problem in the book and give the angle traveled by the mass m . The angle traveled is related to the distance s by s = r . We start by calculating the force F acting on m . This consists of two compo- nents, the horizontal force necessary for keeping the mass in a circular orbit and a vertical necessary for keeping the mass from falling: F = q ( mg ) 2 + m ( v 2 /r ) 2 (1) The acceleration of the particle along its circular path is therefore a t =- k F/m (2) From our standard relationship vdv = ads , we then have the relationship be- tween distance s 1 and velocity v 1 , given an initial velocity v : vdv = a t ds (3) vdv =- k q ( g ) 2 + ( v 2 /r ) 2 ds (4)- v q g 2 + ( v 2 /r ) 2 dv = k ds (5) Z v 1 v- v q g 2 + ( v 2 /r ) 2 dv = k Z s 1 ds (6) Z v 2 /rg v 2 1 /rg 1 q 1 + ( v 2 /rg ) 2 d ( v 2 rg ) = 2 k r s 1 (7) The integral on the left hand side is known to be the inverse hyperbolic sine, sinh- 1 x = ln( x + 1 + x 2 ) , so: 2 k r...
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ENG102_SL3 - DATE: October 9, 2011 DUE: October 14, 2011...

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