A particle moves upward on the circular helix rt cos ti si

A particle moves upward on the circular helix: r(t) = (cos t)i + (sin t)j + t k for

0 =< t < = 2 pi under a force: F(x,y,z) = (-zy)i + (zx)j + (xy)k. Find the work done on a particle by the force.

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Solution

dr= -sintdt + costdt +dt dw=F.dr cost=x sint=y t=z dw = tsin^2t + tcos^t +sintcostdt integrate W =1/2t^2 + 1/2sin^2t limits 0 to 2pi W=2pi^2