Physics Archimedes Principle Distance an object sinks

In summary, when placed in water, a block of wood measuring 2.2m by 2.5m with a depth of 3.6m and a weight of 102KN will sink 52.5% of the water due to its density of 525 kgm-3 compared to the density of water at 1000 kgm-3. To find the distance it will sink, we can use the formula d = (pB/pw)h where d is the distance it sinks, h is the height of the object, pB is the density of the object, and pw is the density of water. Alternatively, we can also calculate the draft of the block using Archimedes' Principle, which
  • #1
nwmyname
8
0

Homework Statement


A block of wood measures 2.2m by 2.5m with depth 3.6m with weight 102KN. When placed in water, how far will it sink?

g = 9.81 ms-2
density of water = 1000kg m-3

Homework Equations

The Attempt at a Solution


Volume = 2.2(2.5)(3.6) = 19.8m3
Mass = 102000 / 9.81 = 10398 kg (nearest whole)
Density = 10398 / 19.8 = 525 kg m3

It sinks 52.5% of the water.

How to continue finding how far it will sink?
 
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  • #2
nwmyname said:
It sinks 52.5% of the water.
Please explain what you mean by that statement.
 
  • #3
haruspex said:
Please explain what you mean by that statement.
The density of the object is 525 kgm-3 and the density of the water is 1000 kgm-3 so it must be sink 52.5% into the water?
 
  • #4
nwmyname said:
The density of the object is 525 kgm-3 and the density of the water is 1000 kgm-3 so it must be sink 52.5% into the water?
How much volume is below water?
 
  • #5
nwmyname said:

Homework Statement


A block of wood measures 2.2m by 2.5m with depth 3.6m with weight 102KN. When placed in water, how far will it sink?

g = 9.81 ms-2
density of water = 1000kg m-3

Homework Equations

The Attempt at a Solution


Volume = 2.2(2.5)(3.6) = 19.8m3
Mass = 102000 / 9.81 = 10398 kg (nearest whole)
Density = 10398 / 19.8 = 525 kg m3

It sinks 52.5% of the water.

How to continue finding how far it will sink?
A much more useful application of Archimedes' Principle would be to find out the draft that the block must float at such that the weight of water displaced by the block is equal to the weight of the block itself. The draft of the block is that distance the bottom sinks below the surface of the water, and given the shape of the block, a trivial calculation.
 
  • #6
nwmyname said:
The density of the object is 525 kgm-3 and the density of the water is 1000 kgm-3 so it must be sink 52.5% into the water?
It sinks 52.5% of what into the water? 52.5% of the block?
 
  • #7
d = (pB/pw)h
d is the distance it sinks in the water.
h is the height of the object.
pB is the density of object
pw is the density of water
 

1. What is Archimedes' Principle?

Archimedes' Principle is a law of physics that states that the buoyant force on an object in a fluid is equal to the weight of the fluid that the object displaces.

2. How does Archimedes' Principle relate to the distance an object sinks in a fluid?

According to Archimedes' Principle, the distance an object sinks in a fluid is determined by the weight of the fluid that the object displaces. The more fluid an object displaces, the greater the buoyant force acting on the object, which causes it to sink deeper into the fluid.

3. What factors affect the distance an object sinks in a fluid according to Archimedes' Principle?

The distance an object sinks in a fluid is affected by the density of the fluid, the density of the object, and the volume of the object that is submerged in the fluid. These factors determine the weight of the fluid displaced and therefore the buoyant force acting on the object.

4. Can Archimedes' Principle be applied to all fluids?

Yes, Archimedes' Principle is a universal law of physics and can be applied to all fluids, including liquids and gases.

5. How is Archimedes' Principle used in real-world applications?

Archimedes' Principle is used in many real-world applications, such as shipbuilding, submarine design, and hot air balloons. It is also used in determining the densities of objects and fluids, and in understanding the behavior of objects in fluids.

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