To solve any problem we need to begin by forming a clear picture of the situation.
In these two questions we are attempting to achieve a certain moment change by moving part of the load.
The moment change which we are trying to achieve is equal to the total mass multiplied by the distance we want to move the CofG. We could express this as M x S where M is the total mass and S is the required CofG shift.
We will achieve this by shifting a small part of the mass a certain distance. We could express this moment change which we are going to cause as m x s where m is the mass we move and s is the distance we shift it.
If we do the job properly the moment change we are trying to achieve (M xS) will be equal the moment change we cause by shifting the smaller mass (m x s)
So we will have M x S equals m x s
In the first question we are trying to calculate the mass to be moved, (s), so we rearrange the equation to give
(M x S) / m equals s (sorry my tablet does not appear to have an equals sign)
M is 100000, S is (16 - 15.5) which is 0.5, s is (25 - 10) which is 15
Inserting these number into our equation gives (100000 x 0.5) / 15 equals the mass to be moved to the aft hold.
Adding this to the initial mass of 3000 kg already in the hold gives us the answer.
The second question can be solved in a similar way, but this time we are trying to find the distance we need to move the 300 kg of the 4 passengers. Dividing this by the seat pitch will then give us the number of rows.
Last edited by keith williams; 7th Oct 2018 at 21:05.