Question

A uniform bridge, 20 m long and weighing 40000 N is supported by two pillars located 3.0 m from each end. If a 19600 N car is parked 8.0 m from one end of the bridge, how much force does each pillar exert?

Answer 1

Let the forces on two pillars are N1 and N2

so we will have force balance equation as

$N_1 + N_2 = 40000 + 19600$

$N_1 + N_2 = 59600 N$

also by torque balance we will have

$N_2\times L = 40000 ]times \frac{L}{2} + 19600 \times 8$

here we know that

L = 20 m

$N_2 (20 m) = 40000 (10 m) + 19600 (8 m)$

$N_2 = 27840 N$

$N_1 = 59600 - 27840 = 31760 N$