Example$-7$: A person does knee extension exercises with a mass of $\backslash (11\backslash$mathrm$\{$~kg$\}\backslash$left$(\backslash$mathrm$\{$~W$\}\_\{0\}\backslash$right$)\backslash )$ attached at the ankle as shown. The free body diagram indicates the forces acting on the leg. Measurements indicate that the subject has height $\backslash (=1\mathrm{.}8\backslash$mathrm$\{$~m$\}\backslash )$ and mass $\backslash (=75\backslash$mathrm$\{$~kg$\}\backslash ).$ Assume that the patellar tendon attaches at a distance of $10$ cm from the knee joint $($i$.$e$.$ distance $\backslash (\backslash$mathrm$\{$a$\}=\backslash )10$ cm $)$ at an angle of $\backslash (\backslash$theta$=120\backslash )$ to the lower leg and that the mass attached at the ankle is a point mass centered at the ankle joint.

Using the anthropometric tables, estimate:

a$)$ the distances b$,$ c

b$)$ the weight of the lower leg and foot, $\backslash (\backslash$mathrm$\{$W$\}\_\{1\}\backslash )$

c$)$ the radius of gyration of the lower leg and foot about the knee

d$)$ the moment of inertia of the lower leg and foot about the knee

If the leg is held still such that the angle $\backslash (\backslash$beta$=45\backslash ),$

e$)$ calculate the force in the tendon $(\backslash (\backslash$mathrm$\{$F$\}\_\{\backslash$mathrm$\{$M$\}\}\backslash )).$

f$)$ calculate the magnitude and direction of the joint reaction force $\backslash (\backslash$left$($F$\_\{\backslash$mathrm$\{$J$\}\}\backslash$right$)\backslash ).$