In order to solve this problem, use the following equations and steps shown: \begin{align} &\cssId{Step1}{ΣF = 0}\\[3px] &\cssId{Step2}{ΣF_{x axis} = F-N_G }\\[3px] &\cssId{Step3}{N_G = F = \frac{mgx}{h} }\\[3px] &\cssId{Step4}{N_G = \frac{mgx}{\sqrt{L^2-x^2}} }\\[3px] &\cssId{Step5}{ΣF_{y axis} = 0 }\\[3px] &\cssId{Step6}{ N_P = mg }\\[3px] \end{align}