Problem $7$: In the figure below, consider that the bike $+$ rider

system is moving forward at a steady speed. The brakes are not

engaged. At the instant shown, the $100$ kg rider of the bicycle is

dividing their weight between the seat and the pedal equally, as

shown. The bike's mass is $8$ kg and its weight is equally

distributed between the two axles.

a$)(4$ points$)$ Construct the free body diagram of the whole

bike. If you need to assume any force or moment that is

not shown but are necessary for constructing the diagram,

please highlight them in your diagram and explain why

they were necessary in the diagram.

b$)(3$ points$)$ Construct the free body diagram of the

subsystem consisting of the rear wheel and the rear

sprocket $($but not the chain$).$ From this, determine the

minimum friction coefficient between the tire and the

ground that would$+$ be needed to keep the wheel turning

without spinning.

c$)(5$ points$)$ Construct the free body diagram of the

subsystem consisting of the two sprockets, the chain, and

the pedal $($but not the wheels or the bike frame$).$ The force

on the other pedal $($not shown$)$ is to be neglected. From

this, report the tension in the chain at this instant.

d$)(3$ points$)$ If the wind drag experienced by the system is $10$

N $,$ what will be the forward acceleration of the system?