Final answer:
The maximum load a steel cable with a radius of 1.5 cm can support, given a maximum stress of 10⁸ N/m², is approximately 70786 N.
Step-by-step explanation:
To determine the maximum load a steel cable can support without exceeding its stress limit, we must start by calculating the cable's cross-sectional area given its radius of 1.5 cm, then use the maximum stress value to calculate the load. The maximum stress that the cable can endure is given as 10⁸ N/m².
The formula to calculate the cross-sectional area (A) of the cable is:
A = π × r²
For a radius (r) of 1.5 cm, which we convert to meters (0.015 m), the area becomes:
A = π × (0.015 m)²
A = π × 0.000225 m²
A ≈ 0.000706858 m²
Next, to find the maximum load (F), we use the formula where stress (σ) equals force (F) divided by area (A):
σ = F / A
Substituting the given maximum stress and the calculated area, we get:
F = σ × A
F = 10⁸ N/m² × 0.000706858 m²
F ≈ 70785.8 N
Therefore, the maximum load the cable can support without exceeding the stress limit is approximately 70786 N.