How Do You Calculate the Volume of a Floating Object?

[x2017]

Homework Statement

If a 5kg object floats in water (density=1000 kg/m³) with 20% of it's volume above the surface of the water, what is the volume of the object?

Homework Equations

Archimedes' Principle = the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and it acts in the upward direction at the centre of mass of the displaced fluid.

density=mass/volume

The Attempt at a Solution

If the weight of the object is equal to the amount of fluid displaced the I was thinking that I need to find that and then I am not sure if the volume of fluid displaced would also equal the volume of the object or not... Any pointers for this question would be greatly appreciated!

 

[SteamKing]

Homework Statement

If a 5kg object floats in water (density=1000 kg/m³) with 20% of it's volume above the surface of the water, what is the volume of the object?

Homework Equations

Archimedes' Principle = the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and it acts in the upward direction at the centre of mass of the displaced fluid.

density=mass/volume

The Attempt at a Solution

If the weight of the object is equal to the amount of fluid displaced the I was thinking that I need to find that and then I am not sure if the volume of fluid displaced would also equal the volume of the object or not... Any pointers for this question would be greatly appreciated!

How can the volume of water displaced by the object not equal the volume of the object which is submerged?

Suppose that the 5 kg object has a constant mass density ρ. Since 20% of the volume of the object is above the surface of the water, what can you infer about the weight of the object?

 

[x2017]

How can the volume of water displaced by the object not equal the volume of the object which is submerged?

Suppose that the 5 kg object has a constant mass density ρ. Since 20% of the volume of the object is above the surface of the water, what can you infer about the weight of the object?

That the water weighs more? Or the object is less dense?

 

[SteamKing]

That the water weighs more? Or the object is less dense?

By Archimedes Principle, if the object is floating, the weight of the water displaced = the weight of the object.

 

[x2017]

By Archimedes Principle, if the object is floating, the weight of the water displaced = the weight of the object.

So 5kg of water is displaced... Do I find the volume of 5kg of water and does that also equal the volume of the object?

 

[x2017]

Sorry for double posting, but:

The weight of a floating object is equal to the amount of fluid displaced. Therefore, since the object weighs 5kg, 5kg of water is displaced.

density=mass/volume
volume=mass/density
volume=5kg/(1000kg/m³)
volume=0.0005m³

The 5kg of water has a volume of 0.0005m³, therefore the object has a volume of 0.0005m³.

Could someone please let me know if this is correct? I feel like there is a flaw in my reasoning at the end. Thanks!

 

[SteamKing]

Sorry for double posting, but:

The weight of a floating object is equal to the amount of fluid displaced. Therefore, since the object weighs 5kg, 5kg of water is displaced.

density=mass/volume
volume=mass/density
volume=5kg/(1000kg/m³)
volume=0.0005m³

The 5kg of water has a volume of 0.0005m³, therefore the object has a volume of 0.0005m³.

Could someone please let me know if this is correct? I feel like there is a flaw in my reasoning at the end. Thanks!

Check your arithmetic. 1 liter of fresh water = 1 kg. How many liters are there in 1 cubic meter?

 

[x2017]

Check your arithmetic. 1 liter of fresh water = 1 kg. How many liters are there in 1 cubic meter?

There are 1000L in 1 cubic metre.

So the volume is .5 litres?

 

[SteamKing]

There are 1000L in 1 cubic metre.

So the volume is .5 litres?

No. If the object weighs 5 kilograms and there is 1 kg of water in each liter, how many liters of water are displaced by the object?

You didn't check your arithmetic like I advised previously.

 

[x2017]

No. If the object weighs 5 kilograms and there is 1 kg of water in each liter, how many liters of water are displaced by the object?

You didn't check your arithmetic like I advised previously.

5 litres. I did check my work. I don't understand the question. If I could figure out how to fix it I wouldn't be asking for help.

 

[SteamKing]

5 litres. I did check my work. I don't understand the question. If I could figure out how to fix it I wouldn't be asking for help.

5 liters ≠ 0.0005 m³, which is why I asked you to check your arithmetic.