The discussion centers on the relationship between bath oil depth and soap buoyancy, specifically when a soap bar of thickness 2.09 cm, submerged 1.50 cm in water, is affected by the addition of bath oil with a specific gravity of 0.639. Participants clarify that the buoyant forces from both the water and the oil must be considered to determine the new equilibrium position of the soap. The total volume displaced by the soap must equal the combined buoyant forces from both liquids, leading to a mathematical relationship that can be solved for the depth of the oil layer.
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DDS said:This is what i have:
Fbw=mg
dw*vw*g=ds*vs*g
density of soap=717.7
Fbo + Fbw2 = mg
(0.639*XA*9.81) + (100*YA*9.81) = d*v*g
cancel terms and you get
(0.639*X) + (1000*Y) = d
i know you relate them through thickness of the soap but how?
DDS said:I know i made a mistake in righting it, its supposed to be:
(0.639*X) + (1000*Y) = ds * 0.0209
then form here is used my two equaions to find x and y but i seem to be getting the answer from which i originally thaught it would be:
i know x+y =0.0209 m
and i also know that
x=23.45 - 1564.9y
which i got from simplyfiying the very first equation in this post.
from there i found that
Y= 0.0149m
and X=5.91e-3
then wouldn't the depth of the oil layer be equal to my value from X or am i missing something??