Problem $3(25$ pt$)$

Draw the three free body diagrams below. Label all forces properly and draw vectors in their proper direction.

Assume that:

The cyclist has just started pressing down with his right foot on the pedal with force $P($so the cyclist on the bicycle hasn't moved yet$).$

The masses of the cyclist and bike are mc and mb$,$ respectively.

The cyclist is sitting on the seat $($seat forces $Sx$ and $Sy)$ and pressing down and forward on the handlebars $($handlebar forces $Hx$ and $Hy).$

The internal friction in the bicycle bearings can be neglected.

Ascume that N$1$ and N$2$ are the normal forces at rear and front

Does the weight of the cyclist effect the normal force on the wheels? Explain your answer.

Does the weight of the cyclist appear in the FBD of the bicycle? Explain your answer.