what forces are acting on a bike?

Fishy

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Consider a biker riding on level ground as shown. She wants to have the maximum forward acceleration possible, which means experiencing the maximum horizontal force without her wheels slipping.

To analyze this problem correctly, we need to be careful about the forces on the bike wheels. The forces between the road and the back wheel can be different from the forces between the road and the front wheel, and only the back wheel is connected to the drive chain and the pedals. We need to distinguish between these forces in our free body diagram and force equations.

Which of the free body diagrams below is correct for this problem, with the bike and biker accelerating forward? These diagrams are for the biker and the bike combined. In these diagrams, the subscripts G, N, and f refer to the graivitation, normal, and friction forces respectively. The subscripts F and R refer to the Front and Rear wheels. The force labeled "Biker" is the force the biker is exerting to turn the back wheel.
 
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