Post date: Jul 16, 2013 7:20:9 PM
Yesterday I watched the Disney movie, Tangled.
(Warning: small spoilers may be below this line)
Still here? Good.
I found it to be a good movie, except for the bad parts - they really didn't have to start the movie with a song detailing the main character's routine boring life. It just makes the audience feel that the movie is routine and boring, and makes Friday seem like an expansive creative song. Overall though, it was probably the best (and only) movie to borrow plots from a fairytale, Shakespeare's Cymbeline and The Winter's Tale, and Super Mario Brothers at the same time.
While I've been able to watch past movies with a suspension of disbelief (e.g. Iron Man III), in this case it's more like an emulsion of disbelief. So I'll be looking at the physics of the film, focusing on that crazy hair of the main character.
EDIT: hi past self! This article does a much better analysis of the topic below.
Edit #2: this kind of research is the sort that wins you Ig Nobel prizes.
A normal female adult has a mass of, on average, 72 kilograms. This means that, for Rapunzel's hair to hold the weight of Mother Grtham,
her hair must apply an equal force of (72 * 9.8 = 705.6 N) up to counteract the downward force of gravity. (Assuming her hair's weight is negligible (it's ducking magic, after all))
Hair's Ultimate Tensile Strength - the pressure required to break it - is 380 megapascals. From this, we can calculate the cross-sectional area that her hair braid needs to have in order to pull a person up the tower.
705.6 N / 380,000,000 N /m2 = 0.000001857 m2 = 1.856842105 mm2
area = pi * r2, so sqrt(1.856842105 / pi) = 0.768798867 mm radius?!
Even if you agree with the standard operating procedures for steel wire, and use a diameter of hair that could take up to 5 times the force, you'll still only need
705.6 N * 5 / 380,000,000 N/m2 = 0.000009284 m2 = 9.284210526 mm2,
sqrt(9.284210526 / pi) = 1.719086528 mm radius.
I must say, I didn't expect this answer! Does this mean that a tiny braid of hair can actually be enough to pull a person up a tower?
Now, compare with the diameter of steel wire it would take to pull up a person: 1/4-inch-diameter steel wire is more than enough (who knew?!)
(Other people has done more comprehensive analysis, however, I'm afraid of reading them for fear of learning more stuff)
Anyways, I'm also wondering: how much would a massive bundle of hair actually weigh?
I'm going to borrow, of all things, research done to refute a Biblical description of Absalom's hair. It states here that an average blond person would have ~150,000 hairs on one's head, so with each hair having a diameter of ~0.007 cm, and with her hair having a length of 70 feet (number taken straight off the DVD box) or 21.34 m, and with hair's density being 1.3g/cm3, we can calculate the total mass.
(pi * (0.0035)2)cm2 * 2134cm * 150000 * 1.3g/cm3 / 1000g/kg = 16.014545622 kg, which pretty much weighs as much as the weight of a four-year-old toddler.
But of course, since it's a faery tale, none of the above really applies - if these numbers seem weird, just remember: her hair is magic.