Calculating Force of 29.9kg Barbell Underwater

[SnowOwl18]

-----A bodybuilder is holding a 29.9kg steel barbell above her head. How much force would she have to exert if the barbell were lifted underwater?----

Ok...I'm really not sure of this one. I thought maybe the answer was the weight of the barbell (mg) plus the atmospheric pressure at sea level...does anyone know if I'm headed in the right direction? Thanks.

 

[Doc Al]

buoyant force

Consider the buoyant force that the water exerts on the barbell. This force acts upwards, making the barbell easier to lift under water.

 

[SnowOwl18]

most equations say that the buoyant force= density of water x volume of object x gravity. but i do not know the volume...i do know that mass= density x volume...but if that is so, couldn't i theoretically just multiply the mass of the barbell by gravity to get the answer?

 

[Doc Al]

No. One equation uses the density of water; the other, the density of steel. (But you're getting closer.)

 

[SnowOwl18]

Steel...I should've seen that. Well, what I tried to do was find the volume of steel using what I knew... 29.9kg= 7860kg/m^3 x V ...and for that value I got 0.0038m^3...and so I multiplied that by the density of water and then by gravity to get the buoyant force and got 37.28N, but the program says it's wrong. And I thought I was headed in the right direction...lol. Is there another huge mistake I'm making?

 

[Doc Al]

That's the correct value for the buoyant force. So, how does that relate to the force that the bodybuilder needs to exert on the barbell?

 

[SnowOwl18]

Well...the buoyant force is the weight of the displaced water...aha! I have it. You subtract the buoyant force from the force that would normally be exerted above water (mg). Thank you for your help! :D