Question

# Consider a 6-legged water-treader with a body mass of 18 mg (milligrams) and perfectly-non-wetting legs of...

Consider a 6-legged water-treader with a body mass of 18 mg (milligrams) and perfectly-non-wetting legs of total combined length 20 mm standing on a freshwater pond. The body length is 10 mm and the body density is ? = 1200 kg/m3. Consider the mass of the legs to be negligible.

The equation for the upwards surface-tension force that prevents the water-treader from sinking is given by

F = 2γLcos⁡θ

where θ is the angle of contact between the water and the legs, γ is the surface tension of the water, and L is the total length of the non-wetting legs.

[Useful parameters: Freshwater density, ? = 1000 kg/m3; surface tension of water, γ = 0.073 N/m.]

(a) What is the contact angle, θ, between water and a perfectly-non-wetting surface?

θ =

(b) Without considering surface tension forces, what is the apparent weight of this water-treader?

W =  N

(c) What is the minimum length of non-wetting limbs that this water treader NEEDS in order to be able to balance its apparent weight with the surface tension forces? Give your answer in mm.

L =  mm

(d) [difficult] If water-treaders were to scale isometrically, to what length (in mm) could the water-treader grow before its apparent weight could no longer be balanced by surface tension forces?
[Consider that in isometric scaling, the length of the water treader and the length of its limbs grow at the same rate, but also that you are to ignore the mass of the legs in contributing to the mass of the insect.]

L???? =  mm

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