This is a strange one: 1. The problem statement It is known that the strength of the muscles is proportional to the area of their section. In other words, if the muscles are two times more thick, they have four times greater strength.Explain why people cannot grow indefinitely tall. 3. The attempt at a solution I have no idea where to start actually and i'm completely stuck. I would appreciate any help i can get here.
If the muscle is twice as thick and twice as long, how much more is it's volume? What is it's weight proportional to? Does the muscle strength increase faster or slower than the weight it needs to support?
Okay so muscles strength is proportional to the square of the thickness while mass it needs to support is proportional to the cube of the thickness. Mass grows faster so there's a limit. that's clear. the question then asks: The size of some planet is 10 times greater than that of the earth. Its mass is 1000 times greater than the mass of the Earth. Suppose that the tallest person on the Earth is 2 meters high, what would be the height of the tallest man living on the surface of this planet? Okay so I know using the 2 meters high, I need to find some sort of constant that relates strength to mass. not too sure how to do this. and i'm thinking i need to somehow incorporate the different "g" that will be observed because of the different size of the planet. aah so confused. Help please!
I didn't realize there is a direct relationship to one's muscle size and how tall they are! It would seem that their height is independent of their muscle size. Otherwise all the small people in the world would start bodybuilding and get taller! :rofl:
but i don't see how i can relate the weight of the person to the thickness of the muscle. that's the part that's keeping me from doing this.
The accn due to gravity at the surface of a spherical body is GM/R^2. If that of planet is g’, whose mass is Mp and radius Rp, then g/g’ = (Me/Mp)(Rp/Re)^2, where suffix e stands for earth. The ratios are given. The max weight/muscle area should be constant if the muscles on both planets are made of the same material. Suppose Lp and Le are the max heights. I’ll use the symbol ~ for “is proportional to”. Mass ~ volume = L^3 for same density. We can write, maximum weight/muscle area ~ mg/L^2 ~ L^3*g/L^2 = L*g. So, L*g is constant. Then, Lp*g’ = Le*g => Lp = Le*g/g’. Plug in the values now. (By the size I presume the volume is meant, which is giving a very small height indeed on the other planet, because g’ of the other planet is very high. Confirm whether they mean radius is 10 times. Anyway, the method is what matters.)