Find the work done going around a unit circle in the xy-plane
a) counterclockwise from 0o to 180o
b) clockwise from 0o to -180o, doing against a force field given by:

Question

Find the work done going around a unit circle in the xy-plane
a) counterclockwise from 0o to 180o 
b) clockwise from 0o to -180o, doing against a force field given by:

anonymous · Answer

$$F = \frac{ -i y }{ x^{2} + y^{2}  } + \frac{ -j x }{ x^{2} + y^{2}  }$$

Note that the work done depends on the path

anonymous · Answer

@ivanmlerner @sandra

anonymous · Answer

$$W=-\int\limits_{x(t_{0})}^{x(t_{1})}F.rdl$$Use cilindrical coordinates and you get:$$F=\frac{-\sin(\theta)}{r^2}i+\frac{-\cos(\theta)}{r^2}j$$$$dl=r d \theta$$Since r=1,

anonymous · Answer

Sorry, didnt finish, clicked post without wanting to, just a sec

anonymous · Answer

And its r, not r^2 on the denominator

anonymous · Answer

|dw:1350708883820:dw|$$F.r=\left| F \right|\cos \left( 2\theta+\frac{\pi}{2}\right)$$From now on its just math.

anonymous · Answer

Do you understand it?