Question

A steel wire of diameter 1 mm can support a tension of 0.2 kN. A steel cable to support a tension of 20 kN should have diameter of what order of magnitude?

Short answer

As a result, the cable's diameter is $=1\text{mm}\sqrt{100}$

$~1\text{cm}$

Step-by-step solution

Step 1:

The diameter of the steel wire is 1mm in this case. $={10}^{-3}\text{m}$

$F_1=0.2\text{kN}$is the tension force.$=0.2\times {10}^3\text{N}$

The cable has a tension force of$F_2=20\text{kN}$.

Because all of the wires are bundled together, they can withstand almost identical stress.

As a result, the number of wires$=\frac{20\text{kN}}{0.2\text{N}}$

The cable's cross-sectional area is equal to the difference of the cable's diameter.

As a result, the cable's diameter is$=1\text{mm}\sqrt{100}$ $~1\text{cm}$