Will the scuba diver sink or float

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The discussion revolves around calculating the buoyant force acting on a scuba diver who displaces 65.0L of water and weighs 68.0kg. The diver's weight is calculated to be 670N, and an attempt to find the buoyant force using Archimedes' principle results in an incorrect value of 6.4X10^8N due to a miscalculation in converting liters to cubic meters. Participants highlight the importance of accurate unit conversion, noting that 65L equals 0.065m^3, not 6.5X10^4m^3. Ultimately, the diver would float if the buoyant force exceeds her weight, but the initial calculation was flawed.
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Homework Statement


A scuba diver and her gear displace a volume of 65.0L and have a total mass of 68.0kg. What is the buoyant force on her and will the diver float or sink.


Homework Equations



FB=pFVg

The Attempt at a Solution


The first thing I did was find the weight of the diver as w=mg=68.0kgX9.8m/s2=670N
Then I tried to find the buoyant force using archemedes' principal (FB=pH20Vg
I used the given density as 103 kg/m3, the volume of water displaced is 65.0L, which I converted to m3 by using the factor of 103L/1m3 to get 6.5X104m3. The equation then becomes
(103kg/m3)(6.5X104m3)(9.8m/s2)
and I get 6.4X108N, which is greater than mg, so the diver would float.

I'm wondering if this is correct or not

Edit: Forgot to mention, I'm not too concerned with sigfigs, as long as the answer is withing a reasonable variance the teacher will give me credit.
 
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That buoyant force is awfully large. Check your L to m^3 conversion
 
rmiller70015 said:

Homework Statement


A scuba diver and her gear displace a volume of 65.0L and have a total mass of 68.0kg. What is the buoyant force on her and will the diver float or sink.


Homework Equations



FB=pFVg

The Attempt at a Solution


The first thing I did was find the weight of the diver as w=mg=68.0kgX9.8m/s2=670N
Then I tried to find the buoyant force using archemedes' principal (FB=pH20Vg
I used the given density as 103 kg/m3, the volume of water displaced is 65.0L, which I converted to m3 by using the factor of 103L/1m3 to get 6.5X104m3. The equation then becomes
(103kg/m3)(6.5X104m3)(9.8m/s2)
and I get 6.4X108N, which is greater than mg, so the diver would float.

I'm wondering if this is correct or not

Edit: Forgot to mention, I'm not too concerned with sigfigs, as long as the answer is withing a reasonable variance the teacher will give me credit.

How much does 65L of water weigh?
 
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Salt water, or fresh water?

Not that it matters much in this case, but it matters when you dive.
 
Borek said:
Salt water, or fresh water?

Not that it matters much in this case, but it matters when you dive.

Good point! :smile:
 
If there are 1000 L in 1 m^3, how can 65 L = 65000 m^3?

That's the amount of water displaced by a large ship.
 

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