Expert: John Locke - 5/11/2010

Question
I need help with a project that I have for science. I need to prove one of Wonder Woman's, Marvel comic book superhero, superpowers wrong (or right if possible). I chose to do her superstrength. I found that she can lift 200 tons (or 200,000 pounds). I want to prove this wrong. So far, I have the following. Can you tell me if I'm on the right track or direct me to another approach? Anything would be helpful.

Okay, here's what I have so far:

One of the most common yet desired superpowers is superhuman strength.  Wonder Woman is one superhero that has this power. She is said to have lifted one hundred tons (equivalent to 200,000 pounds). A human’s muscles can lift a lot of weight by having adrenaline. The process of releasing this hormone, adrenaline (epinephrine), starts with the stressor. The stressor is activated when a human sees something dangerous or scary to them (a relative pinned beneath a car, for example). This then stimulates the hypothalamus, which is an area of a human’s brain that is responsible for maintaining the balance between stress and relaxation in one’s body.  When it is stimulated, it sends out a chemical signal to the person’s adrenal glands. This activates the sympathetic system, which sends the body in to an excited state. These glands release the adrenaline, which allows muscles to contract. It allows them to contract by allowing blood to flow more easily to your muscles, which means that more oxygen is carried to your muscles. This makes our muscles contract, or tighten, which is how weight can be lifted. Therefore, when confronted with extreme stress, humans can involuntarily use our muscles beyond their normal use.
As humans, we build our muscles by lifting weights and adding stress to our muscles. When muscles are subjected to mechanical stress greater than their usual level, they grow stonger. Muscle needs to experience overload to reach a new adapted level of muscle. Wonder Woman trained, just like this, to gain her strength.
The Olympic record (as of 2007) for a dead lift is 455 kilograms, or about 1,000 pounds. Maximum strength for weight lifting is close to the height of the person doing the lifting in meters squared.

Answer
Thanks for using AllExperts. It's actually fairly straightforward to disprove the ability of a human to live anywhere near 100 tons; it requires some math, which I have included here. Your intro so far is entirely reasonable--I would note that epinephrine increases the ability of muscle to contract by stimulating the uptake of glucose from the blood stream--this increases the fuel available to muscle--and increasing heart rate, which increases the oxygen available to muscle. Viewing something that is perceived as a threat is relayed from the sensory cortex of the brain through the hypothalamus to the brain stem--the locus coeruleus--which actually stimulates the release of epinephrine from adrenergic neruons and the adrenal gland.

The strength of a muscle is proportional to its cross-sectional area:
Strength~A

Since the cross-section of a muscle is roughly circular, we can say that

Strength~r^2

where r is the radius of the muscle in cross-section. More generally, since the surface area of the cross-section is also a function of r^2, we can say that any increase in the radius of the muscle would cause the surface area to increase as the square of the radius.

Now, it is known that the mass of a muscle depends not on the square of the cross-sectional radius, but on the cube of the radius. In other words,

Mass~r^3

Since r^3 increases at a greater rate that r^2, an increase in cross-sectional area sufficient to achieve enough strength to lift 100 tons would require a muscle mass so great that the person would likely collapse underneath their own weight. The weight of their muscles would break their bones; they would certainly be unable to lift any additional weight--they would probably not be able to even support their own weight. Since muscle strength depends on cross-sectional area, we cannot get around the fact that a muscle with wide cross-section is necessarily a heavy one.