Giant ants (or other insects) sometimes feature in science-friction movies. Supp

Question

Giant ants (or other insects) sometimes feature in science-friction movies. Suppose that an ant is "scaled up" from its original size to something much larger, in such a way that all of its linear measurements (height length of legs, thickness of legs, etc.) are changed by the same factor; this means that the ant still has the same body shape and proportions as before, just bigger. A typical ant is about 0.5 cm long. Suppose we scale up an ant so that it is 2 m long. Assume that the ant's body is still made of the same biological materials, so that each cubic centimeter of the big ant weighs the same as a cubic centimeter of small ants (i. e., it has the same density). (a) By what factor would the mass of the ant increase i.e., what is the ratio M_/M_ ? Explain your reasoning and show any calculations you make. (b) What would happen to the tensile stress on each of the ant's legs when the ant is standing? Find the ratio (stress) _big ant/(stress)_small ant. Explain your reasoning and show any calculations you make. (c) Based on your result from part (b), explain why the big ant would have difficulty surviving.

Explanation / Answer

For increasing every dimension to 4 times the original dimension
the volume of the insect would depend on the dimension cube
so new volume = 4^3 * original volume = 64* original volume

so, new mass/new volume = old mass/old volume
new mass = old mass * 64
a) M big ant/ M small ant = 64
b) stress = force/area
now, as mass increased 64 times, force increases 64 times, but area increases 16 times too
so, stress big ant/stress small ant = 64/16 = 4 times
c) Big ant would need higher stress to walk, making it difficult for its bones to withstand the weight and needing more energy to walk, hence difficult for it to survive

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