Consider the $11,000kg$ tractor below. Assume $40\%$ of the weight is on the front axle. To $($somewhat unrealistically$)$ simplify the analysis, sum moments about the point where the rear wheel touches the ground and assume that the interactions with the ground do not provide any moments on the tractor. Start with NO pull force.

a$.$ What is the vertical ground contact force $(N)$ on each front tire?

b$.$ Assuming the weight is shared evenly, what is the contact force on each rear tire?

c$.$ How far $(mm)$ is the center of gravity in front of the rear axle?

d$.$ Assume the tractor is providing $60$ kW to a load pulled at $8$ kph $.$ What is the pulling force $(N)?$

e$.$ Assuming the pulling force is strictly horizontal, what is the approximate minimum coefficient of friction needed between the tires and the ground?

f$.$ According to U$.$S$.$ standards $($ASABE S$482)$ the hitching point of a towed implement should be ${19}^{7\text{'}}(\frac{+}{-}{2}^{27})$ from the ground $($see $"$ x $"$ dimension I added$).$ If this load is being towed at the nominal $({19}^{77})$ height, what is the vertical ground contact force on front and rear tires?

g$.$ The Europeans tend to hitch much higher. For example, what are the ground contact forces if the same load is pulled at a height of $38$ in$.$ above the ground?

h$.$ Assume the Europeans decide to add weights using the front $3-$point hitch and that the weights are centered $1500$ mm in front of the center of the front axle. What weight is needed to get $35\%$ of the weight on the front axle when towing the load? What weight is needed to get $40\%$ on the front axle?

i$.$ If you have added those weights, what percentages of the total weight is the front axle carrying when you are not towing the load?