## Related questions with answers

In the Grimms’ fairy tale Rapunzel, she lets down her golden hair to a length of $20$ yards (we’ll use $20 m$, which is not much different) so that the prince can climb up to her room. Human hair has a Young's modulus of about $490 \mathrm{MPa}$, and we can assume that Rapunzel's hair can be squeezed into a rope about $2.0 \mathrm{~cm}$ in cross-sectional diameter. The prince is described as young and handsome, so we can estimate a mass of $60 \mathrm{~kg}$ for him.

(a) Just after the prince has started to climb at a constant speed, while he is still near the bottom of the hair, by how many centimeters does he stretch Rapunzel's hair?

(b) What is the mass of the heaviest prince that could climb up, given that the maximum tensile stress hair can support is $196 \mathrm{MPa}$?

Solution

VerifiedIn this problem, Rapunzel roll's down her hair so that the prince can ascend. The hair has length $l = 20$ m, diameter $d = 2.0$ cm and has Young's modulus $Y = 490 \times 10^{6}$ Pa. The prince has mass $m$ and climbs at a constant speed.

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