Will the scuba diver sink or float

  • Thread starter rmiller70015
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In summary: A scuba diver and her gear would only displace a small amount of water. In summary, when calculating the buoyant force on a scuba diver and her gear, it is important to take into account the density of the water and the volume of water displaced. In this case, the calculated buoyant force was greater than the weight of the diver, indicating that the diver would float. The conversion of 65.0L to m^3 was incorrect, as it should have been 0.065 m^3. It is important to pay attention to units and conversions when solving physics problems.
  • #1
rmiller70015
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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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  • #2
That buoyant force is awfully large. Check your L to m^3 conversion
 
  • #3
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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  • #4
Salt water, or fresh water?

Not that it matters much in this case, but it matters when you dive.
 
  • #5
Borek said:
Salt water, or fresh water?

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

Good point! :smile:
 
  • #6
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.
 

Related to Will the scuba diver sink or float

1. What determines if a scuba diver will sink or float?

The weight and density of the scuba diver's body, as well as the amount of air in their scuba tank, will determine if they will sink or float.

2. Can a scuba diver control their buoyancy while underwater?

Yes, scuba divers can control their buoyancy by adjusting the amount of air in their scuba tank and using specialized equipment, such as a buoyancy compensator device (BCD).

3. Will a scuba diver always float to the surface?

No, a scuba diver may not always float to the surface. If they are negatively buoyant (their body and equipment are heavier than the surrounding water), they will sink. It is important for scuba divers to maintain neutral buoyancy to stay at their desired depth.

4. How does water temperature affect a scuba diver's buoyancy?

Water temperature can affect a scuba diver's buoyancy by affecting the density of the water. Cold water is denser than warm water, so a scuba diver may need to add more weight to their equipment to maintain neutral buoyancy in colder water.

5. What is the role of air in determining a scuba diver's buoyancy?

The air in a scuba tank is what allows a scuba diver to breathe underwater, but it also plays a crucial role in determining their buoyancy. As the diver breathes, they consume air and become lighter, causing them to rise. To counteract this, they can release air from their BCD to maintain neutral buoyancy.

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