In this question, we've got a lorry wanting
to get weighed across two weighing scales,
one at the front and one at the back. Now
we need to think about the forces acting on
the lorry. By Newton's Third Law, in that
the force exerted on the lorry by each weighing
scale is equal to the forces exerted by the
lorry on each weighing scale. And we know
those forces because we know their readings
on the weighing scales, m1 and m2. So the
forces acting upwards on the lorry are m1g
at the front and m2g at the back. The other
force acting on the lorry is its weight, which
acts downwards from the middle, and is Mg,
where M is the total mass of the lorry, the
thing we want to find out. Since the lorry
is not accelerating anywhere, we know that
the resultant force on it must be zero, and
we can use this to find the total mass of
the lorry.
