Homework Help: Physics Archimedes Principle Distance an object sinks

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1. Feb 19, 2016

nwmyname

1. The problem statement, all variables and given/known data
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

2. Relevant equations

3. 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?

2. Feb 19, 2016

haruspex

Please explain what you mean by that statement.

3. Feb 19, 2016

nwmyname

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. Feb 19, 2016

Staff: Mentor

How much volume is below water?

5. Feb 19, 2016

SteamKing

Staff Emeritus
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. Feb 19, 2016

haruspex

It sinks 52.5% of what into the water? 52.5% of the block?

7. Aug 29, 2016

Benjamin Chang

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