A steel girder AB has weight 210 N - Edexcel - A-Level Maths Mechanics - Question 5 - 2006 - Paper 1

Using the moments about point A to find the length AB:

Let d be the distance from A to C (90 cm), and let AB = 120 cm. The moments about A can be set up as follows:

$(R \cdot d) = (W \cdot AB)$

Substituting the known values, we can rearrange to:

$210 \cdot 90 = 70 \cdot (120)$

Calculating the left side, we find: $18900 = 2100$

So, we verify that indeed: $AB = 120 ext{ cm}$

In this scenario, the tension in the cable at C is now three times the tension at A:

Let the tension at A be T again, so:

$T_C = 3T$

Using a similar moment approach:

Setting the moments about point A gives:

$210 + W = 3T \cdot 60$

Substituting T = 70 N gives:

$210 + W = 3 \cdot 70 \cdot 60$

Solving for W: $W = 3 \cdot 70 \cdot 60 - 210 = 12600 - 210 = 12390$

Thus, the value of W is: $W = 30 ext{ N}$