(c) A non-uniform ladder PQ is 12m long and is balanced at 4m from the end P. When a load of 150 N is hanged at the end Q; the ladder balances at 6m from P. Calculate the weight of the ladder.
To find the weight of the ladder, we can use the principle of moments. The moment of an object is the product of its weight and the distance from a reference point.
Let's assume the weight of the ladder is W. We need to calculate this weight.
In the first situation, the ladder is balanced at 4m from the end P. This means that the total clockwise moment is equal to the total anticlockwise moment. The anticlockwise moment is due to the weight of the ladder, which is W, acting at 12m from P. Therefore, the clockwise moment is due to the load of 150N acting at 4m from P. Mathematically, we can express this as:
W * 12 = 150 * 4
Simplifying this equation gives us:
W = (150 * 4) / 12
W = 600 / 12
W = 50 N
So, the weight of the ladder is 50 N.