Final answer:
The force on pillar A is 6.0 × 10^3 N, and the force on pillar B is 8.4 × 10^4 N.
Step-by-step explanation:
To find the forces acting on each pillar, we need to consider the equilibrium of forces. The weight of the bridge acts downward and is balanced by the upward forces provided by the pillars. Since the lorry is stationary and not moving, the forces acting on each pillar can be determined using a force diagram.
The weight of the bridge is 5.0 × 104 N, and the weight of the lorry is 3.0 × 104 N. Since the lorry is 4.0 m from pillar A, the weight of the lorry provides a clockwise torque about pillar B. To maintain equilibrium, the force on pillar B needs to be greater than the force on pillar A. We can determine the forces on each pillar using the torque equation:
Torque = Force × Distance
For pillar A:
3.0 × 104N × 4.0m = Force on pillar A × 20m
Force on pillar A = (3.0 × 104N × 4.0m) / 20m
Force on pillar A = 6.0 × 103N
Since the weight of the lorry provides a clockwise torque, the force on pillar A is smaller.
To find the force on pillar B, we can use the fact that the sum of the vertical forces must be equal to the weight of the bridge plus the weight of the lorry:
Force on pillar A + Force on pillar B = Weight of bridge + Weight of lorry
6.0 × 103N + Force on pillar B = 5.0 × 104N + 3.0 × 104N
Force on pillar B = (5.0 × 104N + 3.0 × 104N) - 6.0 × 103N
Force on pillar B = 8.4 × 104N
So, the force on pillar A is 6.0 × 103N, and the force on pillar B is 8.4 × 104N.