Answer
a) The normal force exerted on the front wheel is $1.6\times10^5N$
b) The normal force exerted on each rear wheel is $4.2\times10^5N$
Work Step by Step
We take the axis of rotation to be at the front wheel, so the normal force $N_f$ here does not create torque. Let's examine the torque created by the other forces.
- The weight of the jet produces a counterclockwise torque $\tau_w=Wl=10^6\times12.6=1.26\times10^7N.m$
- Normal force from 2 rear wheels produces a clockwise torque $\tau_r=-N_rl=-15N_r$
The jet is in equilibrium, so these two torques balance each other: $$15N_r=1.26\times10^7$$ $$N_r=8.4\times10^5N$$
The normal force at the rear wheels is distributed equally between the wheels, so the force on each wheel is $\frac{N_r}{2}=4.2\times10^5N$
Summing the forces:
$$N_f+N_r-W=0$$ $$N_f=W-N_r=10^6-8.4\times10^5=1.6\times10^5N$$
