Need help answering problems related to Buoyance/Buoyance Force

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The discussion revolves around two buoyancy-related homework problems. The first problem involves calculating the force required to keep a 100kg man submerged in seawater, considering his density and the specific gravity of seawater. The second problem focuses on determining the buoyant force on a 6.6 m^3 helium balloon in air, using the density of air. Participants suggest starting with Archimedes' principle and emphasize the importance of correctly applying the buoyant force formula. Clarifications on the calculations indicate that the expected answer may require a negative sign to reflect the force needed to keep the man submerged.
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I have two homework problems that I am unable to answer related to buoyancy/force. Please help! Thanks!

1. How much force (in Newtons) does it take to hold a 100kg man completely under water in the ocean? His density is 903 kg/m^3, and the specific gravity of sea water is 1.07.

They give the following hint: Buoyant force is greater than the weight: B.F. = Weight + Force Down

2. What is the buoyant force in N on a 6.6 m^3 helium balloon in air at standard conditions? The density of air is 1.3 kg/m^3

They give the following hint: According to Archimedes you only need to know the weight of the air displaced.
 
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Sam,
what have you got so far and where are you stuck? If you haven't started yet, then I think Archimedes' law is a good starting point.
 
Here's what I have so far...

I have the following, but I know my answer isn't correct because it's an online course and will let you know when you are correct:

Let:

Mm = mass of man in kg (given at 100 kg)
Vm = volume displaced by man in m^3 = Mm/Dm
Sg = specific gravity of seawater (given at 1.07)
Dw = Density of pure water 1 gm/cm^3 = 1000kg/m^3
Ds = Density of seawater
Fb = Buoyancy force
g = acceleration of gravity in m/s^2 = (9.8 m/s^2)

Here's how I tried to solve:

Fb = Vm*Dw*g
= (Mm/Dm)*Sg*Dw*g
= (100 kg/903kg/m^3)*1.07*(1000kg/m^3)*9.8m/s^2 N

Ok, so the buoyant force exceeds his weight. To keep him submerged you'd have to push him down with the difference force F=1161 - 980 or about 181 N.

What did I do wrong?
 


Hmmm... looks OK to me. With the following changes, which don't change the result:

Fb = Vm*Sg*Dw*g
= (Mm/Dm)*Sg*Dw*g
= (100 kg/903kg/m^3)*1.07*(1000kg/m^3)*9.8m/s^2 no N

Since they say B.F. = Weight + Force Down, maybe they expect the answer to have a minus sign. Suggest you try that.
 
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