Find the work done by the force F(x, y) = 2xyi + 4y2j acting along the piecewise smooth curve consisting of the line segments from (-2,2) to (0,0) and from (0,0) to (2,3).

Question

amistre64 · Answer

it looks to me kinda like you want the magnitude of force in the direction of the line segments given the results of the Force vector

amistre64 · Answer

|dw:1352131244373:dw|

amistre64 · Answer

looks to me like the magnitude along the line is equal to: F cos(a)

amistre64 · Answer

$$F = \sqrt{(2xy)^2+(4y^2)^2}$$ $$cos(\alpha) = \frac{a\cdot b}{|a|~|b|}$$ $$cos(\alpha) = \frac{<2xy,4y^2>\cdot <1,-1>}{\sqrt{(2xy)^2+(4y^2)^2}~\sqrt2}$$ $$F~cos(\alpha) = \frac{2xy-4y^2}{~\sqrt2}$$ $$F~cos(\alpha) = \sqrt2~(xy-2y^2)$$ $$Work=\int_{-2}^{0}\int_{2}^{0}F~cos(\alpha)~dy~dx$$ maybe

amistre64 · Answer

if its right, then the same concept for the other line segment