Question

Two stretched cables both experience the same stress. the first cable has a radius of 3.3x10-3 m, and is subject to a stretching force of 290 n. the radius of the second cable is 5.5x10-3 m. determine the stretching force on the second cable.

Answer 1

To calculate the stretching force on the second cable, use the stress formula—stress = force/area—and apply the proportion based on the radii and forces of the two cables, since the same stress is experienced by both.

Step-by-step explanation:

The student's question involves calculating the stretching force on a second cable, given that both cables undergo the same stress. To find this force, we can use the formula for stress (stress = force / area), and because the stress is equal for both cables, we can set up a proportion using the radii and forces of the two cables.

For the first cable with a radius of 3.3 x 10-3 m and a force of 290 N:

Stress = 290 N / (π * (3.3 x 10-3 m)2)

For the second cable with a radius of 5.5 x 10-3 m, we have:

Stress = F / (π * (5.5 x 10-3 m)2)

Since the stress is the same for both, setting these equal allows us to solve for the force F:

290 N / (π * (3.3 x 10-3 m)2) = F / (π * (5.5 x 10-3 m)2)

You can the cross-multiply and divide to find F, which represents the stretching force on the second cable.

Answer 2

Stress is the force per unit area or pressure. Let's find the stress for the first cable.

S = F/A = 290 N/ [π*(3.3×10⁻³ m)²] = 8476571.808 Pa

We equate this to that of the second cable.

8476571.808 Pa = F/[π*(5.5×10⁻³ m)²]
Solving for F,
F = 805.56 N