Volume of a Floating Object

In summary: The conversion from liters to cubic meters is not 1:1. It is 1:1000.In summary, to find the volume of the 5kg object floating in water with 20% of its volume above the surface, we can use Archimedes' Principle which states that the weight of the object is equal to the weight of the fluid displaced. By converting the density of water to kg/m3, we can determine that 5kg of water is displaced by the object. Converting this to liters, we get a volume of 5 liters. However, to find the volume in cubic meters, we must divide by 1000, giving us a volume of 0.005 m3 for the object.
  • #1
x2017
84
1

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!
 
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  • #2
x2017 said:

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?
 
  • #3
SteamKing said:
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?
 
  • #4
x2017 said:
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.
 
  • #5
SteamKing said:
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?
 
  • #6
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!
 
  • #7
x2017 said:
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?
 
  • #8
SteamKing said:
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?
 
  • #9
x2017 said:
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.
 
  • #10
SteamKing said:
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.
 
  • #11
x2017 said:
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.
 

1. What is the definition of "volume of a floating object"?

The volume of a floating object refers to the amount of space a submerged object takes up in a liquid. It is often measured in cubic units such as cubic meters or cubic feet.

2. How is the volume of a floating object calculated?

The volume of a floating object is typically calculated by measuring its dimensions, such as length, width, and height, and then using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

3. Why is the concept of volume important in understanding floating objects?

The volume of a floating object is important because it directly affects its buoyancy, or ability to float. Objects with a greater volume will displace more water and have a higher buoyancy, while objects with a smaller volume will have a lower buoyancy.

4. Can the volume of a floating object change?

Yes, the volume of a floating object can change depending on factors such as temperature, pressure, and the amount of water it displaces. For example, as an ice cube melts in water, its volume decreases, causing it to float lower in the water.

5. How does the volume of a floating object relate to its density?

The volume of a floating object is directly related to its density. Objects with a higher density will have a smaller volume and therefore displace less water, while objects with a lower density will have a larger volume and displace more water, resulting in a higher buoyancy.

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