Question 7.2: The diagram shows a man of weight 600 N standing on a footbr...
The diagram shows a man of weight 600 N standing on a footbridge that consists of a uniform wooden plank just over 2 m long of weight 200 N. Find the reaction forces exerted on each end of the plank.
The diagram shows the forces acting on the plank.
For equilibrium both the resultant force and the total moment must be zero.
As all the forces act vertically we have
R + S – 800 = 0 ①
Taking moments about the point A gives
(\curvearrowleft ) R × 0 – 600 × 0.5 – 200 × 1 + S × 2 = 0 ②
From equation ② S = 250 and so equation ① gives R = 550 .
The reaction forces are 250 N at A and 550 N at B.
Note
1 You cannot solve this problem without taking moments.
2 You can take moments about any point and can, for example, show that by taking moments about B you get the same answer.
3 The whole weight of the plank is being considered to act at its centre.
4 When a force acts through the point about which moments are being taken, its moment about that point is zero.
