A beam of 20 metres is pivoted at its midpoint with loads at specific points. What load is needed at the extreme left end for equilibrium if a 200 N load is at 5 m from the right and a 300 N load is at 8 m from the right?

To determine the load needed at the extreme left end for equilibrium, we first need to analyze the beam and the positioning of the loads. The beam, which is 20 metres long, is pivoted at the midpoint (10 metres from either end).

Let's establish the distances of the other loads from the pivot:

• The 200 N load is placed 5 metres from the right end, which means it is 5 m from the right end and 15 m from the pivot (10 m - 5 m).

• The 300 N load is positioned 8 metres from the right end, translating to 2 m from the pivot (10 m - 8 m).

Next, we calculate the moments produced by the loads about the pivot:

1. The moment caused by the 200 N load:

[

\text{Moment from } 200 N = 200 , \text{N} \times 15 , \text{m} = 3000 , \text{N m}

]

This moment acts in a clockwise direction.

2. The moment caused by the 300 N load:

[

\text{Moment from } 300 N = 300 \