(II) At depths of 2000 m in the sea, the pressure is about 200 times atmospheric pressure (1 atm

step 1 Once again, welcome to new problem. This time we have, this is like this surface, the water surf

(II) At depths of 2000 m in the sea, the pressure is about...

Key Concepts

Pressure

Pressure is defined as force per unit area and represents the influence that a force distributed over a surface has. In fluids, pressure increases with depth due to the weight of the fluid above, which is crucial for understanding how external forces act on submerged objects.

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at equilibrium due to the gravitational force. It increases linearly with depth and is key to calculating the extreme conditions objects experience in deep water environments.

Bulk Modulus

The bulk modulus is a measure of a material’s resistance to uniform compression. It is defined as the ratio of an applied pressure change to the resulting relative volume change. This concept is essential when determining how much a material, such as iron, contracts when subjected to high external pressures.

Volume Change Under Compression

This concept links the applied pressure and the material's bulk modulus to the resulting change in volume. It involves calculating the fractional reduction in volume using the relationship between pressure increment and the material's bulk modulus, often expressed as a percentage change.

Transcript

00:01 Once again, welcome to new problem.

00:04 This time we have, this is like this surface, the water surface, or you can think of it as the sea.

00:19 And the actual depth is 2 ,000 meters.

00:27 So from sea level up until the bottom is 2 ,000 meters.

00:31 And the change in pressure is 200 times.

00:38 200 times the atmospheric pressure.

00:45 So just think of pat as atmospheric pressure and the pressure itself is one atmosphere.

01:03 Remember one atmosphere is the same as 1 .0 times 10 to the 5 newton a meter squared.

01:16 That's one atmosphere.

01:20 So we have an ion bath sphere.

01:29 Think of it as an ion bath sphere.

01:35 And we want to know by how much the interior space, by how much the interior space changes when you drop it like 2 ,000 meters below sea level.

02:01 And remember, at this point, point right here the pressure is 200 times atmospheric pressure and one atmosphere is 1 .0 times 10 to 5 newton committee squared so we want to know by what percentage so we want by what percentage by what percentage but what percentage does the interior space of the ion change and by ion we mean the ion battle sphere so we're looking for delta v next page we're going to say that delta p is 200 changing pressure the bulk modulus the bulk modulus b is 90 times 10 to the 9 newton per meter squared and it's the same as negative delta p of a delta v0 so it just means the delta v of v0 v0 is the initial volume of the iron this is the change when it goes down and that's just changing volume remember when it goes down you know this thing is a lot of pressure like when it goes down like that when it sinks so it's going to have like a change involved so this is equals to negative delta p over b and then also we could say that delta v or v -not you know ignore this negative sign because now we're dealing with change in volume the negative sign just means that you have a decrease in volume.

04:37 That's all it means.

04:41 So delta v over v is 200 atmospheres minus the original atmosphere.

04:51 You know, i mean think of it this way...

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