The problem involves a bar of soap floating on water, partially submerged, with bath oil added on top. The objective is to determine the depth of the oil layer when the soap's top is level with the oil's surface. The context includes concepts from buoyancy and fluid mechanics.
Participants are actively engaging with the problem, sharing their calculations and interpretations. Some have provided insights into the relationships between the volumes and weights of the fluids involved, while others express confusion about applying these concepts mathematically. There is a recognition of the need to express certain quantities in terms of the cross-sectional area of the soap.
Participants note the specific gravity of the bath oil and the density of water as key factors in their calculations. There is an ongoing discussion about the assumptions made regarding the soap's uniform thickness and the implications of adding the oil on the buoyancy of the soap.
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??