Overhead electricity cables for railway lines are supported by structures like the one shown - Edexcel - A-Level Physics - Question 14 - 2023 - Paper 1

To solve this problem, we need to consider the moments acting around point X.

Step 1: Identify Forces

The forces acting on the electric cable include:

• Weight of the cable:

  $W = mg = 45 ext{ kg} \times 9.81 \text{ m/s}^2 = 441.45 \text{ N}$

• Tension in the cable: T

• The force exerted by rod Y on rod X: F_Y (acting vertically on rod X)

Step 2: Establish the Moment Equation

We will take moments about point X to eliminate T from our calculations. The moment due to the weight of the cable about point X is calculated as:

• The vertical distance from X to the line of action of the weight (at the midpoint of the cable, 1.5 m) is:

  $d = 1.5 imes ext{sin}(35°)$

The total effective distance for the weight:

$d = 1.5 imes 0.5736 \approx 0.8604 ext{ m}$

The moment caused by the weight of the cable about point X is:

$M_W = W \times d = 441.45 \text{ N} \times 0.8604 ext{ m}$

Step 3: Calculate the Moment

The moment due to the weight of the cable about point X:

$M_W = 441.45 \times 0.8604 \approx 379.2 \text{ Nm}$

Step 4: Calculate the Force from Rod Y

Assuming rod Y's angle is also 35°, the distance (lever arm) from point X to Y is 1.3 m. Thus, the moment due to the force exerted by rod Y around point X is:

$M_Y = F_Y \times 1.3 ext{ m}$

Setting the two moments equal gives:

$F_Y \times 1.3 = 379.2$ Consequently, we can solve for F_Y:

$F_Y = \frac{379.2}{1.3} \approx 292.46 ext{ N}$

Thus, the force exerted on rod X by rod Y is approximately 292.5 N.