# Physics

In the Grimms' fairy tale Rapunzel, she lets down her golden hair to a length of 20.0 yards (we'll use 20.0 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 MPa, and we can assume that Rapunzel's hair can be squeezed into a rope about 2.00 cm in cross-sectional diameter. The prince is described as young and handsome, so we can estimate a mass of 60.0 kg for him.

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

What is the mass of the heaviest prince that could climb up, given that the maximum tensile stress hair can support is 196 MPa? (Assume that Hooke's law holds up to the breaking point of the hair, even though that would not actually be the case.)

1. 👍
2. 👎
3. 👁
1. (delta L)/L = (stress)/E

Stress = 4 M g /(pi d^2)

E = 490*10^6 N/m^2
M = 60 kg
d = 0.0200 m)
L = 20 m
g = 9.8 m/s^2
Solve for delta L

For the maximum load question, set
4 Mg/(pi d^2)= max stress = 196*10^6 N/m^2

Since a single hair that is tugged on is often more likely to be pulled out than break, it is quite likely that the overweight prince will pull all her hair out rather than break it.

1. 👍
2. 👎

## Similar Questions

1. ### Bio

Blonde hair (bb) is a recessive trait and brown hair (Bb) is dominant. If both parents have brown hair, what must be true if one of their children have blonde hair? A. Both parents must be hybrid with regard to hair color (Bb) B.

2. ### Algebra

The ratio of the length to the width of a golden rectangle is (1 + √(5):2:.The dimensions of a garden form a golden rectangle. The width of the garden is 12 feet. Find the length L of the garden. Round your answer to the nearest

3. ### English

What is the significance of “The Magic Bonbons” in literary history? The Magic Bonbons a.It is a morality tale from the age of Colonial America. b.It is a story about ambition from the period of realism and naturalism. c.It is

4. ### Health

The hair on your body is able to help keep you healthy in many different ways.Your hair (1) protects your scalp from sunlight and provides insulation from the cold. (2) hair from nostrils, ears, and ______ prevents debris from

1. ### history

Which popular ancient Egyptian folk tale recounts the wanderings of its hero? The Epic of Gilgamesh The Tale of Sinuhe

2. ### Probability

For hair color, Brown (B) is a dominant trait and Blond (b) is a recessive trait. If one parent has pure blond hair and one parent has hybrid brown hair, complete the Punnett square and questions that follow. a) What is the

3. ### greek philosophy and history

Aristotle taught his students to follow the a. Golden Rule c. golden mean b. Golden Fleece d. none of these

4. ### Biology

Blonde hair (bb) is a recessive trait and brown hair (Bb) is dominant. If both parents have brown hair, what must be true if one of their children have blonde hair? A. Both parents must be hybrid with regard to hair color (Bb) B.

1. ### Science

The height of a plant is dependent upon? 1)it's genes 2)it's environment 3)both it's genes and it's environment 4)neither it's genes nor it's environment I think #1 In humans, the allele for curly hair and the allele for straight

2. ### Science

When hair is combed with a hard rubber comb, the hair becomes positively charged because the comb A. Transfers protons to the hair B. Remove electrons from the hair C. Transfers electrons to the hair D. Remove both times from the

3. ### Literature

What are some similarities between the Wife of Bath's Tale and The Merchant's tale (by chaucer)?

4. ### Math

if an 8 inch wide rectangle is to approach the golden ratio, what should its length be?