A particle moves along line segments from (0,0,0) to (1,0,0) to (1,2,1) to (0,2,

Question

A particle moves along line segments from (0,0,0) to (1,0,0) to (1,2,1) to (0,2,1) to (0,0,0) under the influence of a force field F(x,y,z)=<z^2,2xy,4y^2> measured in Newtons.

a) Draw the curve C and the upward oriented plane S that this piecewise-smooth, simple, closed curve C forms the boundary of. Allso draw the orientation of C.

b) Determine the equation of plane surface S.

c)Assuming that x,y, and z are measured in meters use Stokes' theorem to calculate the work done in moving the particle once around path C.

Explanation / Answer

c)

the work done by the force on the particle as a line integral over the path taken by the particle. Symbolically, this is

? F ? ds
c

where ds = (dx)i + (dy)j + (dz)k and C is the path taken by the particle.

For your F, after performing the dot product, we end up with

?(z

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