What equations are needed to solve this wheelchair kinetics problem?

[Lalaland]

Homework Statement

A man is pushing the wheelchair having combined mass of 80kg with center of gravity at CG. The mass of each rear wheel is 1.6 kg and moment of inertia 0.1kgm^2. Friction coefficient for all wheels 0.6 . Find maximum acceleration of the wheelchair without slippage between the wheel and ground and without separation of front wheel from the ground. Ind propulsion force applied by hand to make such acceleration.

Homework Equations

Considering separate FBD of one rear wheel the equation of moment about point O can be used.

The Attempt at a Solution

First I considered total force in x -direction:
Ftot = f2-f1=ma to find max acceleration. But to find the propulsion force I don't know which equation is relevant

 

[Simon Bridge]

Instead of trying to remember which equations to use, try to identify the kinds of processes that are involved - then relate them to the geometry of the wheelchair.
You can see that you will need both linear forces and moments to properly analyse this situation.
You will also want to have some expression for the contact forces involved.