Will the scuba diver sink or float

[rmiller70015]

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

F_B=p_FVg

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 (F_B=p_H20Vg
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.

 

[Hollumber]

That buoyant force is awfully large. Check your L to m^3 conversion

 

[berkeman]

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

F_B=p_FVg

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 (F_B=p_H20Vg
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?

 

[Borek]

Salt water, or fresh water?

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

 

[berkeman]

Salt water, or fresh water?

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

Good point!

 

[SteamKing]

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.