Is T=PV-M the Correct Formula for Calculating Buoyancy in Water?

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The formula T=PV-M is discussed in relation to calculating buoyancy, where P represents the density of the surrounding fluid, V is the volume of the object, and M is its mass. The object in question can float due to trapped air and is capable of carrying an additional load of 10 kg. There is confusion regarding the relationship between the formula and the lecturer's assertion that 1Kcm^3 of air can lift 1 kg, with some participants suggesting that the formula and the lecturer's claim do not contradict each other. Clarification is provided that the tension T can represent either an upward force partially supporting the buoyant object or a downward force, affecting the calculations of buoyancy needed to balance the total downward forces. Ultimately, the discussion emphasizes the importance of correctly interpreting the forces involved in buoyancy calculations.
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I believe that T=PV-M. P is density of fluid surrounding the object, v is volume of object and M is the mass of object.

So i have this object which is able to float due to air trapped inside it. This object is able to carry an extra load of 10 kg. So my formula would be,

T= [p*(vol of object + vol of air + vol of load)]-(mass of object + mass of load+mass of air),

Am i right?

However, my lecturer taught us that 1Kcm^3 of air would be able to float up/lift up a mass of 1kg. I find that this idea contradicts with the formula given. So u guys have any idea on who is right?
 
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T would be the tension of object floating in water
 
malek340 said:
I believe that T=PV-M. P is density of fluid surrounding the object, v is volume of object and M is the mass of object.

So i have this object which is able to float due to air trapped inside it. This object is able to carry an extra load of 10 kg. So my formula would be,

T= [p*(vol of object + vol of air + vol of load)]-(mass of object + mass of load+mass of air),

Am i right?

However, my lecturer taught us that 1Kcm^3 of air would be able to float up/lift up a mass of 1kg. I find that this idea contradicts with the formula given. So u guys have any idea on who is right?
You are mixing up your weight forces and your mass, btw. But your formula looks OK. It doesn't seem to clash with what your lecturer is saying. 1000cm3 has a mass of 1kg (weight 10N) so those figures imply that your upthrust will support a weight of 10N (mass= 1kg). In your formula, T would be zero- implying the total bouyancy would be neutral. He is just cutting a corner and saying that the density of the object being suspended is so high, compared with the air, that it is displacing a negligible amount of extra water.
 
This is my object specifications
Mass of object= 18kg
Mass of load=10kg
Target tension(t)=4kg

So this is what he mentioned, the total mass of the object, together with the load of 10kg, would be 32kg(18+10+4).
So he assumed that 32kcm^3 of air would make it float with 4kg lift/tension.

However by using the formula T=pV-m, the volume of air that i would obtain would be different.
I can't seem to find a reason to tally the answers
 
Can you confirm that T is the tension in a tether, holding the object under water? (It's not clear in the OP). If that is the case, the bouyancy force must balance the downwards forces of (18+10+4)g.

If T is an upwards force, partially supporting the bouyant object, the downwards forces are (18+10)g so, to find the bouyancy force needed, you subtract the 4g tension force from that.
 

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