Changing Moments

I have two separate questions regarding moments changing:

1)

If a bus drives across a bridge supported at two points (the bus starts from the origin, O, and the bridge is supported at s₁ from the origin and s₂ from the origin by 2 contact forces - this is all 1D) what happens to the magnitudes of those contact forces (obviously s₁ and s₂ cannot change), and/or to the bridge itself, as the bus travels across the bridge? Regard the bus as a point particle with weight m₂g and the bridge itself as a 1D body with weight m₁g.

(1)
Suppose that you have a uniform bridge of length $l$ where the supports are at either end of the bridge - if you like, at $x = 0$ and $x = l$.

The forces at the supports $F_0$ and $F_l$ must satisfy $F_0 + F_l = (m_1 + m_2)g$ for there to be no net force, which is the first requirement for equilibrium.

The second requirement is for there to be no unbalanced moment. In general, if we let the position of the bus be $x$ then taking moments about the axis through O eliminates $F_0$ to leave us with $m_2 gx + m_1 g(\frac{l}{2}) = lF_l$.

Now clearly if $x$ is small then $F_l$ is small, and vice versa. The force $F_0$ does the opposite of $F_l$. By symmetry, the contact forces must be equal when the bus reaches the centre of the bridge. You can confirm this by putting $x = \frac{l}{2}$ above.

Of course, I have not given you exactly what you wanted; I have only considered the special and, I would think, most usual case. If you decide to put the supports elsewhere, you just need to adjust the second equation.

I see - so speaking purely qualitatively, the closer the bus is to one of the supports, the greater the proportion of the total contact force required is provided by that one. Does this apply even if the supports do not start from either end? And if we say support 1 is at x₁ and 2 is at x₂, then is it correct that between x=0 and x=x₁, and between x=x₂ and x=l, we cannot have equilibrium and both contact forces are 0 (the bridge will turn)?

I see - so speaking purely qualitatively, the closer the bus is to one of the supports, the greater the proportion of the total contact force required is provided by that one. Does this apply even if the supports do not start from either end? And if we say support 1 is at x₁ and 2 is at x₂, then is it correct that between x=0 and x=x₁, and between x=x₂ and x=l, we cannot have equilibrium and both contact forces are 0 (the bridge will turn)?