Physics Archimedes Principle Distance an object sinks

AI Thread Summary
A block of wood measuring 2.2m by 2.5m and 3.6m deep, weighing 102KN, will sink based on its density of 525 kg/m³ compared to water's density of 1000 kg/m³. The calculations show that the block displaces water equal to its weight, leading to a draft calculation to determine how far it sinks. It is established that the block sinks 52.5% into the water, but clarification is needed on what this percentage refers to. The discussion emphasizes using Archimedes' Principle to find the draft, which is the distance the block sinks below the water's surface. Overall, the focus is on understanding the relationship between the densities and the volume of water displaced.
nwmyname
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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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nwmyname said:
It sinks 52.5% of the water.
Please explain what you mean by that statement.
 
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?
 
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?
 
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.
 
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?
 
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
 

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