#### Answer

$$\frac{815,360}{3} \mathrm{N}\approx 271786.7~N$$

#### Work Step by Step

We calculate the force as:
\begin{align*}
F&=w \int_{0}^{2} y(y) d y+w \int_{2}^{6} 2 y d y\\
&=\left.w \frac{y^{3}}{3}\right|_{0} ^{2}+\left.w y^{2}\right|_{2} ^{6}\\
&=\frac{8 w}{3}+32 w\\
&=\frac{104 w}{3}\\
&=\frac{104}{3} (800)(9.8)\\
&=\frac{815,360}{3} \mathrm{N}
\end{align*}