A beam having a length of 20 metres is pivoted at its mid point. A 200 newton load is located at a point 5 m from the right hand end of the beam. A 300 newton load is located at a point 8 m from the right hand end. In order for the beam to be in equilibrium, what load is required at the extreme left end of the beam?

let the load be x N

10x = 5(200) + 2(300)
10x = 1600
x = 160 N

To find the required load at the extreme left end of the beam for it to be in equilibrium, we need to consider the principle of moments. The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.

In this case, we have two loads acting on the beam - a 200 N load located 5 m from the right-hand end (let's call it Load 1) and a 300 N load located 8 m from the right-hand end (let's call it Load 2).

Let's assume the load at the extreme left end of the beam is L N. Since the beam is pivoted at its midpoint, it means that the distance between the pivot and the left end is the same as the distance between the pivot and the right end (10 m).

Now, let's calculate the moments created by each load. The moment of a force about a pivot point is equal to the force multiplied by the perpendicular distance from the pivot to the line of action of the force.

The moment created by Load 1 can be calculated as follows:
Moment1 = Load1 x Distance1 = 200 N x (10 m - 5 m) = 1000 Nm

Similarly, the moment created by Load 2 can be calculated as follows:
Moment2 = Load2 x Distance2 = 300 N x (10 m - 8 m) = 600 Nm

Since the beam is in equilibrium, the sum of the clockwise moments (Moment1) must be equal to the sum of the anticlockwise moments (Moment2 and the moment created by the load at the extreme left end of the beam).

Thus, we can write the equation as follows:
1000 Nm = 600 Nm + L x (10 m - 0 m)

Simplifying the equation:
1000 Nm - 600 Nm = 10 L Nm

400 Nm = 10 L Nm

Dividing both sides by 10 Nm:
40 N = L

Therefore, in order for the beam to be in equilibrium, a load of 40 N is required at the extreme left end of the beam.