Mechanics Tutorial 5  Moments and Bridges
Contents 
At its simplest, a bridge is a plank of wood placed between two supports. As the plank of wood has a mass, it must also have a centre of mass. At this level, we will assume that the plank is totally regular, and its centre of mass is exactly in the middle.
Notice that at each end there is a pivot, around which we will need to take moments. Even if there were no actual pivot mechanism, we treat the bridge as if there were. If the plank broke in the middle, the right hand half would turn about the right pivot, and the left half around the left pivot.
So let us have a look at the moments around each pivot:

Worked Example

Answer 
Now let's do an example with two vehicles on. The principles are the same.
Worked Example
On the bridge shown in the diagram above, what are the forces on the abutments A and B? Use g = 9.8 N kg^{1}. 
Answer To work out the force on A, we need to take moments about B.
To work out the force on B, we need to take moments about A:
Note that we have given our answer to 2 significant figures, as the data are to 2 s.f. 
Give your answer to an appropriate number of significant figures. Use g = 9.8 N kg^{1}. 
Many other problems involving moments can be solved easily by modelling them as bridge problems, for example:
A table with objects on it;
A motorbike (the centre of mass is not in the middle in this one);
A lorry carrying a load;
A bridge crane.