Thread: work - calculus
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Old November 1st, 2007, 06:48 AM
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Quote:
Originally Posted by kittycat View Post
given the force vector field F = <y,a> .
Find the work in moving an object through the vector field along the closed curve C formed by the arc of the ellipse x=acost , y=bsint, lying in the first quadrant, the x-axis, and the y-axis.

Please help me. thank you very much.
have you checked the previous post about work?
so,
r(t) = x(t)i + y(t)j = (a \cos t)i + (b \sin t)j
where t is from 0 to \, \frac{\pi}{2}
and
F(x,y) = yi + aj

note that
W = \int_C F \cdot dr = \int_C <y,a> \cdot <dx,dy>
\, = \int_0^{\frac{\pi}{2}} y(t)dx(t) + a dy(t)

can you continue?
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