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When we talk about the cross-sectional area of a cable, we are referring to the area of the face of the cable that is perpendicular to its length. Imagine slicing a cable like slicing a loaf of bread.
This slice, which would look like a circle, is the cross-sectional area. For a round cable, the formula for calculating this area is quite straightforward. It is given by the formula: - - \[ A = \pi r^2 \] Here, \(A\) is the cross-sectional area, \(\pi\) is a mathematical constant approximately equal to 3.14159, and \(r\) is the radius of the cable. The radius is simply the distance from the center of the circle to the edge.
So, if you know the radius of a cable, like \(3.5 \times 10^{-3} \) meters or \(5.1 \times 10^{-3} \) meters for our cables, you can easily find the area by plugging the radius into this formula. This area is crucial because it helps us understand how much space is available for the force to act upon the cable.
The larger the area, the more the cable can handle forces without stress levels becoming too high.

The stretching force is a term used to describe the amount of force applied along the length of a material that tends to elongate it. Imagine pulling on both ends of a rubber band; the force you exert by pulling is similar to the stretching force.
In the context of cables, this force is crucial as it determines how much the material can stretch before it starts to permanently deform or fail. The unit of force, the Newton (N), gives us a measure of the strength of the pull that the cable is enduring.
For instance, the first cable experiences a stretching force of 270 N. This is a substantial force, and knowing this helps us calculate the resulting stress each cable experiences. The stretching force on the second cable can be determined using the concept of stress because both cables are under the same stress state.

Stress is a key concept in material science. It describes how a force is distributed over an area within a material and gives us a sense of the intensity of the internal forces that the material experiences. Stress is mathematically given by the formula: - - \[ \sigma = \frac{F}{A} \] Where \( \sigma \) represents stress, \( F \) is the force applied, and \( A \) is the cross-sectional area.Stress is measured in pascals (Pa), which is equivalent to one Newton per square meter.
This formula allows us to calculate the stress experienced by any material if we know the applied force and the area over which it is applied. Importantly in our case, both cables experience the same stress, meaning that the ratio of force to area is identical for both.
So, when you calculate the stress for the first cable using its known force and area, you can apply that same stress value to determine the force acting upon the second cable by solving for the unknown force. This approach leads us to finding that the second cable must have a different force acting on it to maintain the same stress level due to its different cross-sectional area.