Bouyant force and apparent weight

[chantalprince]

1. The problem statement, all variables and given/known data


This question is continued from a problem that I have already solved. This is what I know from the previous problem that will be helpful:

r= 0.20 m
roh of solid sphere= 850 kg/m^3
mass sphere= 3.94 x 10 ^-5 kg

I also have 2 apparent weights that I solved for when the tension in the system is
a. 150 N ----> Normal force (apparent weight) Fn = -1.49 x 10^2
b. 0 N -----> Fn = -3.86 x 10^-4 N

(Hopefully those are correct)


Now- the problem I came for help on:

A room is partially filled with water with a sphere in it and the sphere is on a scale. What percentage of the sphere must be immersed in the water in order to achieve the same apparent weights as above (a and b).
And- What percentage of the sphere must be immersed to achieve an apparent weight of zero?


2. Relevant equations

% immersed = V immersed/ V total = roh obj/roh fluid
Bouyant force (Fb) = roh x V x g
Fn = mg + ma (a = O)

And from a full body diagram I have this:

Fn + Fb - mg = ma (whch is zero)



3. The attempt at a solution

Well....I really am not sure what to do. One fact that I know and I think will help me is that if an object is say 90% underwater, then the roh of the object is 90% of the fluid....

I need a kick in the right direction please.

[Delphi51]

Fn + Fb - mg = ma (whch is zero)
Start with this, the 3 forces acting on the sphere. Fill in the detailed formula for each force.

[chantalprince]

Ok- here's what I got, but Im not sure what this implies...

mg + roh x V x g -mg = 0

mg cancels and I end up with roh x V x g = 0