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* L = 40000 ]times (L)/(2) + 19600 * 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`