An aeroplane with a two wheel nose gear and four main wheels rests on the ground with a single nose wheel load of 500 kg and a single main wheel load of 6000 kg. The distance between the nose wheels and the main wheels is 10 meter. How far is the centre of gravity in front of the main wheels?
Ok so the best way is to draw it. For this question assume the nose wheels are on the datum. So you should have a diagram (a simple line will do) on the far left will be the nose wheels and on the far right the main wheels at 10m.
The formula for CG is momentum/mass, and momentum is calculated by mass x distance from the datum.
So:
Total mass at the nose wheel (at the datum): 1000kgs
Main wheel total mass: 24,000kgs
Let's apply the mom/mass formula...but wait, whats the total momentum?
To calculate the momentum the main wheel has (mass x arm) 24,000kgs x 10m = 240,000
Now, the nose wheel is located on the datum, so it's distance is 0. 1000 x 0 = 0.
Now we have the momentum and mass, let's calculate the CG.
CG = mom/mass
=240000/25000
=9.6m
So the CG is located 9.6m aft of the datum. And to answer the question, the CG must be 0.4m in front of the main wheels.