TBR Physics Fluids and Solids Passage I

[dennis-brodmann]

I have a question from TBR Physics Fluids and Solids Passage I (Stresses and Strains).

A 1-m^3 block of aluminum sank to the bottom of a lake of depth 750 m. By how much did the block shrink?

The way it was solved was through applying the bulk modulus equation:
B=-P/(deltaV/V)
Where B for aluminum is 7.5 * 10^10 Pa.

The solution says that we need to use the applied pressure, and for a liquid at depth h, the pressure of any object increases due to the weight above it.
According to them, that pressure applied to the block would be P=(rho_water)gh.

My reasoning, which may have been twisted based on EK 1001 Physics, was that not only would the fluid pressure contribute, but atmospheric pressure would as well.

Can someone tell me why that is not the case?

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[dennis-brodmann]

From EK, they said with for every 1 m in depth for a fluid, pressure increases by 1 atm.
Based on this, I solved the problem and got the right answer. This made me suspicious though. Does the 1 m to 1 atm, only apply if the fluid is water?

 

[gongshow89]

Think about the block at the surface...What is the pressure that is "shrinking it"? Atmospheric right! Atmospheric pressure is always applied. Now move the block 750 m below water, what is the pressure that is shrinking it? Atmospheric + pgh...so the only difference is pgh. Therefore, pgh is the pressure that accounts for the difference in size between the block at the surface and the block 750 m below water. You're right that atmospheric pressure is applied, but it's always applied and can be cancelled out in this case. Hope I answered your question and cleared it up.

 

[dennis-brodmann]

Think about the block at the surface...What is the pressure that is "shrinking it"? Atmospheric right! Atmospheric pressure is always applied. Now move the block 750 m below water, what is the pressure that is shrinking it? Atmospheric + pgh...so the only difference is pgh. Therefore, pgh is the pressure that accounts for the difference in size between the block at the surface and the block 750 m below water. You're right that atmospheric pressure is applied, but it's always applied and can be cancelled out in this case. Hope I answered your question and cleared it up.

I get it!! Thanks for your help!