A football $($soccer$)$ player can kick the ball with about $4kN$ of force. Suppose an athlete accidentally kicks their competitor's tibia instead of the ball. This injury may be modeled by the diagram below, where the kick is represented by force $F.$

Assume that the load is applied directly in the middle of the tibia. For the sake of simplicity, model the bone as a solid beam with $2cm2cm$ square cross$-$sectional area. Note that the pin and roller in the model do not induce reaction moments. Use $E=16$GPa.

$($a$)$ Draw a free body diagram $($FBD$)$ including all external forces.

$($b$)$ Draw a FBD with exposed face in the region between $x=0$ and $x=20cm.$ Find $V(x)$ and $M(x)$ in that region.

$($c$)$ Sketch $V(x)$ and $M(x)$ along the length of the bone. Label the axes and include the values you found in $($b$).$ Note that because of symmetry your solutions to part $b$ is sufficient to generate the plot for the full bone.