Rotational Equilibrium

Quote:

Originally Posted by MBrown92

Whilst I'm usually decent at physics this chapter seems to go right over my head. The book problems right now are

"A uniform bridge 20.0m long and weighing 4.00 x 10^5 N is supported by two pillars located 3.00m from each end. If a 1.96 x 10^4 N car is parked 8.00m from one end of the bridge, how much force does each pillar exert?"

I have no idea where to start. They give me a few equations earlier in the chapter but those are all about rotation, and there seems to be no rotation in this problem. I don't exactly know how I'd draw a force diagram here. I know mg, normal force, and all but I'm not sure how I'd find how much force is exerted on each pillar.

Thanks.

let $F_1$ = upward pillar force near the left end of bridge
$F_2$ = upward pillar force near the right end of bridge
$W_B$ = bridge weight
$W_C$ = car weight

let the car be 8 m from the left end

translational equilibrium ...

$\sum F_y = 0$

$F_1 + F_2 - W_B - W_C = 0$

let the point where $F_1$ exerts its upward force be the pivot point for system torques.

rotational equilibrium ...

$\sum \tau = 0$

$F_2(14 \, m) - W_C(5 \, m) - W_B(7 \, m) = 0$

solve for $F_2$ ... then determine $F_1$