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Chapter 6: Problem 24

Spider silk is a remarkable elastic material. A particular strand has spring constant \(70 \mathrm{mN} / \mathrm{m},\) and it stretches \(9.6 \mathrm{cm}\) when a fly hits it. How much work did the fly's impact do on the silk strand?

Short Answer

Expert verified
The work done by the fly's impact on the silk strand is 0.32 Joules.

Step by step solution

01

Conversion of units

Convert the displacement from cm to m. 1 cm = 0.01 m. Thus, 9.6 cm = \(9.6 * 0.01 = 0.096\) m.
02

Substitution

Substitute the spring constant \(k = 70 \, mN/m\) and the displacement \(x = 0.096 \, m\) into the work done formula \(W = 0.5 * k * x^2\). This gives, \(W = 0.5 * 70 * (0.096)^2\).
03

Calculate the work done

Calculate the work done. Therefore, \(W = 0.5 * 70 * (0.096)^2 = 0.32\, mN.m\) or 0.32 Joules (since 1 N.m = 1 Joule).

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