A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 108 N m–2, what is the maximum load the cable can support ?

To solve this problem, we use the formula for stress:

Stress (σ) = Force (F) / Cross-sectional Area (A)

Rearranging the equation to solve for the force:

F = σ × A

Given Data:
Radius of the steel cable, r = 1.5 cm = 0.015 m
Maximum stress, σ = 108 N/m²
Step 1: Calculate the Cross-sectional Area
The steel cable has a circular cross-section, so its area is given by:

A = πr²

Substituting the value of r:

A = π × (0.015 m)²
A = π × 0.000225 m²
A ≈ 0.00070686 m²

Step 2: Calculate the Maximum Load
Using the formula:

F = σ × A
F = (108 N/m²) × (0.00070686 m²)
F ≈ 0.0761 N

Final Answer:
The maximum load the steel cable can support is approximately 0.0761 N.