Oceans on Mars. Scientists have found evidence that Mars may once...

Question

Oceans on Mars. Scientists have found evidence that Mars may once have had an ocean 0.500 km deep. The acceleration due to gravity on Mars is 3.71 m/s^2. (a) What would be the gauge pressure at the bottom of such an ocean, assuming it was freshwater? (b) To what depth would you need to go in the earth's ocean to experience the same gauge pressure?

Accepted Answer

Everyone today, we are going to determine the gauge pressure at the bottom of the ocean of the newly discovered planet and determine the depth of the earth's ocean, where a gauge pressure will record similar values. So we know or it is given in our problem statement that the newly discovered planet has a 1.2 kilometer deep ocean. So I'm just gonna write it down as a church are H is going to be 1.2 kilometer or essentially 1.2 times 10 to the power of three m. And it is also given that the gravitational acceleration is going to be 5.20 m per second squared. Okay, so recall that to calculate for this pressure or pressure under a surface level, we're gonna need this formula right here, which is pressure equals the atmospheric pressure plus H. Rho G. And we can actually calculate the gauge pressure which is essentially just going to be the pressure difference delta P. Which is equals to p minus P A T. M. This p right here, we can actually substituted from this formula. So P is going to be P A T. M plus H rho g minus B A T M. So we can cancel out the P A. T. M. And the gauge pressure is just going to be a church row and G. Awesome. Okay, so let's start solving the first part which is determining the gauge pressure at the bottom of the newly discovered planets ocean. So the gauge pressure as I said previously is the pressure difference. So delta P equals H rho G And the density of the freshwater row of freshwater. Because we assume that the ocean is filled with fresh water is 1000 kilograms per meter cube. So the age is going to be 1.2 times 10 to the power of three m. The row is going to be this which is 1000 kg per meter cube. And the G is going to be the new gravitational acceleration. Don't forget which is the 5.2 m per second squared. Okay, and this will actually give us a gauge pressure of 6.24 times 10 to the power of six pascal's. Remember that all of this unit combined will be considered a pascal. Okay, so that will be our first part and the second part is if we have this gauge pressure here. So Delta P. If delta P 6.24 times 10 to the power of six pascal, what is going to be the depth of the Earth's ocean that will record similar values? So delta piece H. Road G. So what will be the H value that will give us this delta P. So H will then be 6.24 times 10 to the power of six pascal's. We know that the row of seawater is 10 30 kg per meter cube. So I'm just gonna write it down. So H is going to be 6.24 times 10 to the power of six pascal divided by rho divided by G. So H is going to be 6.24 times 10 to the power of six pascal's divided by 30 kg per meter cube. Multiplied by this is going to be the gravitational acceleration of earth, so 9.8 m per second squared. And this will give us a value of 618 m just like so okay, so we know that the gauge pressure is going to be 6. times down to the part of six pascal's and we know that the age is going to be 6 18 m, which is going to correspond to option A just like so. Okay, and that would be all for this particular problem. Let me know if you guys have any questions or please continue and watch other videos on this similar lessons because there are a lot of other videos that will explain and give you guys a better understanding on this. Thank you.

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