15_Ch 19 College Physics ProblemCH19 Magnetism

15_Ch 19 College - Magnetism 19.32 Since the centripetal acceleration is furnished by the magnetic force acting on the ions mv mv 2 qvB = or the

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Magnetism 155 19.32 Since the centripetal acceleration is furnished by the magnetic force acting on the ions, 2 mv qvB r = or the radius of the path is mv r qB = . Thus, the distance between the impact points (that is, the difference in the diameters of the paths followed by the U and the isotopes) is 238 235 U () 238 235 238 235 5 27 19 2 2 23 .00 10 ms kg 238 u 235 u 1.66 10 u 1.60 10 C 0.600 T v drr mm qB ∆= = ×  =−  × ×  or 2 3.11 10 m 3.11 cm d × = 19.33 In the perfectly elastic, head-on collision between the -particle α and the initially stationary proton, conservation of momentum requires that mv 0 αα pp + = while conservation of kinetic energy also requires that ( ) o r v v 00 v 0 vv v = + . Using the fact that 4 p = and combining these equations gives ( ) 4 or p = 0 4 v ++ 3 5 v v = and ( ) 0 35 85 p vv vv =+ = Thus, 0 33 5 3 55 8 8 v v == = After the collision, each particle follows a circular path in the horizontal plane with the
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This note was uploaded on 12/09/2011 for the course PHYS 2020 taught by Professor Staff during the Fall '10 term at FIU.

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