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Unformatted text preview: m f m 1 dm mv 1 = u ln m f m 1 0 = u ln m i m 1 + u ln m f m 1 0 = u ln m i m f m 2 1 m i m f m 2 1 = 1 m 1 = √ m i m f Problem 2 (a) We have d ~ ‘ = 1 · dφ ˆ φ , and φ goes from to 2 π . I ~ F ± ± ± r =1 · d ~ ‘ =Z 2 π k 1 ˆ φ · ˆ φdφ =2 πk 6 = 0 . (b) A conservative force has zero line integral over any closed path. Thus, ~ F is not conservative, since there is a closed path for which the line integral of ~ F is not zero. (c) Recall that d ds arctan s = 1 1 + s 2 .∂W ∂x =k 1 + y 2 x 2 · ²y x 2 ³ = k y r 2∂W ∂y =k 1 + y 2 x 2 · ² 1 x ³ = k x r 2~ ∇ W = k r 2 ( y ˆ ıx ˆ ) = k r (sin φ ˆ ıcos φ ˆ ) =k r ˆ φ. Although it seems that~ ∇ W = ~ F , the potential W is undeﬁned at the origin. In fact, we cannot deﬁne a potential that is welldeﬁned everywhere , and this has to do with the force being nonconservative. 2...
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 Spring '08
 Staff
 Physics, mechanics, Acceleration, Force, MF, 0 MI

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