The structure of the ferris wheel is accelerating the bench downward at ...
[tex]\displaystyle r\left(\frac{2\pi}{T}\right)^{2}=(5\, m)\frac{(2\pi)^{2}}{(8.0\, s)^{2}}=\frac{5\pi^{2}}{16}\,m\,s^{-2}\approx 3.084\,m\,s^{-2}[/tex]
This is about 3.084/9.8 times the acceleration of gravity, so the person's apparent weight is reduced by that fraction, to about ...
[tex](670\, N)\left(1-\dfrac{3.084}{9.8}\right)\approx 459\,N[/tex]
