Question

Based on the scaling laws, how many times greater is the strength-to-weight ratio of a nanotube (D = 10 nm) than the leg of a flea (D = 100 μm)? Than the leg of an elephant (D = 2m)?

Answer 1

To solve this problem we will apply the laws of proportion between the resistance / weight ratio that may occur depending on the cases mentioned. The strength-to-weight ratio for each object is,

For the nano tube,

`(S)/(W) = (1)/(10*10^(-9)) =1*10^(8)`

For the leg of a flea,

`(S)/(W)= (1)/(100*10^(-6))=10000`

For the elephant,

`(S)/(W) = (1)/(2)= 0.5`

From this we can conclude that the resistance / weight ratio of the nano tube is 10 thousand times better than the flea's leg and
`10 ^ 8` times better than the elephant's leg.