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.

Question

Accepted Answer

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

([latex]\curvearrowleft [/latex]) 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.

Question 7.2: The diagram shows a man of weight 600 N standing on a footbr...

Related Answered Questions

A rectangular block of mass 3 kg is placed on a slope as shown. The angle α is gradually increased. What happens to the block, given that the coefficient of friction between the block and slope is 0.6? ...

Verified Answer:

An increasing force P N is applied to a block, as shown in figure 7.39, until the block moves. The coefficient of friction between the block and the plane is 0.4. Does it slide or topple? ...

Verified Answer:

Verified Answer:

A force of 40 N is exerted on a rod as shown. Find the moment of the force about the point marked O. ...

Verified Answer:

A uniform ladder is standing on rough ground and leaning against a smooth wall at an angle of 60° to the ground. The ladder has length 4 m and mass 15 kg. Find the normal reaction forces at the wall and ground and the friction force at the ground. ...

Verified Answer:

Figure 7.32 shows a model for a step-ladder standing on a smooth horizontal floor. i) Draw a diagram to show the forces acting on both rods AB and BC. ii) Explain why the internal forces in the hinge at B are horizontal. iii) Calculate the tension in the string. A woman of mass 56 kg stands on a ...

Verified Answer:

Two children are playing with a door. Kerry tries to open it by pulling on the handle with a force 50 N at right angles to the plane of the door, at a distance 0.8 m from the hinges. Peter pushes at a point 0.6 m from the hinges, also at right angles to the door and with sufficient force just to ...

Verified Answer: