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Will the scuba diver sink or float

  • #1

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.
 

Answers and Replies

  • #2
30
0
That buoyant force is awfully large. Check your L to m^3 conversion
 
  • #3
berkeman
Mentor
56,506
6,405

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?
 
  • #4
Borek
Mentor
28,305
2,688
Salt water, or fresh water?

Not that it matters much in this case, but it matters when you dive.
 
  • #5
berkeman
Mentor
56,506
6,405
Salt water, or fresh water?

Not that it matters much in this case, but it matters when you dive.
Good point! :smile:
 
  • #6
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,666
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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