Originally Posted by **disclaimer**
$\displaystyle W=\frac{1}{2}F_R\cdot{R}$
Am I approaching the problem correctly? Thanks. |

The equation for the line forming the top of the boundary is

$\displaystyle F = \frac{F_R}{R} \cdot r$

and the work done is

$\displaystyle W = \int_0^RF~dr$

(The applied force F and dr are in the same direction.)

So we have

$\displaystyle W = \int_0^R \frac{F_Rr}{R}~dr$

$\displaystyle W = \frac{F_R}{2R} \cdot R^2 + 0$

$\displaystyle W = \frac{1}{2}F_R R$

(Or you could simply find the area of the triangle, as I suspect you did.)

-Dan