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Unformatted text preview: f ( r ) + x 2 r df dr + y 2 r df dr + z 2 r df dr (8) = 3 f ( r ) + r df dr since r 2 = x 2 + y 2 + z 2 . (d) From part (c), ∇ · r r n-1 = 3 r n-1 + r ( n-1) r n-2 = ( n + 2) r n-1 (9) 4. (a) The work integral is W = Z F · d r = Z (-ydx + xdy ) (10) including the path W =-Z 1 ydx + Z 1 xdy (11) In the ﬁrst integral, we have to specify the value of y as x ranges from 0 to 1 (in this case y = 0). For the second integral, we specify the value of x = 1, so that W =-Z 1 dx + Z 1 1 dy = 1 (12) (b) In this case we specify y = 1 in the ﬁrst integral and x = 0 in the second, giving W =-1 (13) Clearly, for this force, the work done depends on the choice of path. 2...
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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.
- Spring '10