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Found in: Page 382

### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271

# 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?

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

$~1\text{cm}$

See the 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.$=0.2×{10}^{3}\text{N}$

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$\text{}=\frac{20\text{kN}}{0.2\text{N}}$

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

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