Exploring Pressure on Human Bones and Giant Leg Strength

[e^e]

Hi
Two questions,
a) how does pressure (in N/cm^2) on the cross section of a human bone change if the length (i'm assuming the length of the person) would increase 10 times ?
b) How big would a giant have to be so it's legs can support a pressure of 1000 N/cm^2 with a cross section area of 8 cm^2 ? (1 kg = 10 N)
ok, for b) i assumed it's just a matter of obtaining how much force would be generated, so it would be 8000 N , so the giant would be 800 kg. right?
but how do i go about doing a) ?, i thought of assuming for example a 190 cm male would weigh about 80kg in average, which gives 800 kg after multiplying the height by 10. but i would still need cross section area for it. I'm sure there is a better way to do this.
Thanks for any help.

 

[HallsofIvy]

You are leaving a lot unsaid. Do you mean that all linear distance are increased 10 times (so that cross section area is increased by 100 times and volume by 1000 times)? It's not clear to me why the pressure on a cross section would increase at all or why it would be a constant increase. Are you assuming a constant force on the increased cross section? If you were talking about the femur (leg bone), there would be a lot of weight increase above it that would result in a lot of force increase. If you are talking about a neck bone, there would be relatively little increase in force for a similar increase in cross section area. If you are talking about an ulna (forearm bone) while the forearm is lying on a table, there would not be any increase in force at all.

 

[Architeuthis Dux]

I would like to address the questions in the following manner:

a) The pressure on the cross section of a human bone is directly proportional to the weight of the person and inversely proportional to the cross-sectional area of the bone. Therefore, if the length of a person were to increase by 10 times, their weight would also increase by 10 times, assuming the same body composition. This would result in a 10 times increase in pressure on the bone. However, the cross-sectional area of the bone would also increase in proportion to the length, which would offset the increase in pressure. In order to accurately calculate the new pressure, we would need to know the specific bone and its dimensions.

b) Your assumption for part b) is correct. To determine the size of the giant, we can use the formula Pressure = Force/Area. Therefore, for a pressure of 1000 N/cm^2, we would need a force of 8000 N (1 kg = 10 N). This would require a giant with a weight of 800 kg.

To calculate the cross-sectional area, we can use the formula Area = Force/Pressure. Therefore, for a force of 8000 N and a pressure of 1000 N/cm^2, we would need a cross-sectional area of 8 cm^2.

I would also like to mention that these calculations are based on ideal conditions and do not take into account factors such as bone density, muscle strength, and overall body composition. In reality, the pressure on human bones and the strength of giant legs can vary greatly depending on these factors. Further research and experimentation would be needed to accurately determine these values.