Question

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/m^{3}. 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 = 2γLcosθ

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/m^{3}; 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

Answer #1

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 9 mm
and the body density is ?ρ = 1200 kg/m33. 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
???=2??cos?,Fst=2γLcosθ,
where ?θ is the angle of contact between the water and the legs,...

Consider a 6-legged water-treader with a body mass of 23 mg
(milligrams) and perfectly-non-wetting legs of total combined
length 20 mm standing on a freshwater pond. The body length is 12
mm and the body density is ρρ = 1200 kg/m33. 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
Fst=2γLcosθ,
where θ is the angle of contact between the water and the legs,...

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