A 1.0-m-diameter vat of liquid is 2.0 m deep. The pressure at the bottom of the vat is 1.3 atm. What is the mass of the liquid in the vat?

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Hey, everyone in this problem, we have a uniform cylindrical glass barrel of radius, 0.2 m used to store wine. If the wine has a depth of 0.5 m and the pressure at the deepest point is 1.06 times 10 of the exponent five pascals. We're asked to determine the mass of the wine stored in that barrel. If you have four answer choices all in kilograms. Option A 301 option B option C 60.2 and option D 15. we want to find the mass of the wine. Let's think about some equations that would allow us to calculate the mass. You know, we're given the size of this glass barrel. So we can probably find the volume as we have some information about volume. We're looking for maths. Let's recall that we can write the density row is equal to the mass and divided by the volume V. OK. So the mass M can be written as the density row multiplied by the volume V. OK. We said we can calculate the volume knowing the radius of the cylinder and the depth. OK. What about the density? How can we calculate the dens? We're given information about pressure. So let's think about the relationship between pressure and density. Some recall that the pressure P OK, at a particular depth, it's gonna be equal to peanut. The atmosphere of pressure plus row multiplied by G multiplied by H or row is our density G is the acceleration due to gravity. And H is that, so we're giving the information we need, we have the pressure, maybe the atmospheric pressure is a constant that we can look up at a table. In our textbook G is the acceleration due to gravity. We're given the depth and so we can calculate growth. OK. So let's go ahead substitute in our values and find growth. We have 1.06 times 10 to the exponent five cal the pressure at the deepest point is gonna be equal to 1.013 tend to be exponent five pascals. But what's the density row multiplied by the acceleration due to gravity? 9.81 m per second squared multiplied by the depth of 0.5 m we wanna solve for row. So we're gonna move this 1.013 times 10 to the exponent five pascals to the left hand side by subtracting. This is gonna give us 4700 pascals on the left hand side. And then on the right hand side, we still have row multiplied by 9.81 m per second squared, multiplied by 0.5 m. We can divide by our 9.81 multiplied by 0.5 to isolate for row. And we have a pascal divided by meters per second squared, divided by meters. OK. This is gonna leave us with kilogram per meter cubed. If we work it out, we get 0.206 kilograms per meter cubed. All right. So we found our density using the pressure we were given in the problem. Now, we need to find the volume and that's that other piece of information we need for our mass equation. OK. And the volume of the cylinder recall is gonna be pi are screwed multiplied by the in this problem, we're given that the radius is 0.2 m. The depth is 0.5 m. So we have that the volume is gonna be high multiplied by 0.2 m squared, multiplied by 0.5 m. And we're gonna leave this with the pie just to avoid some extra round off error here. And we get that this is gonna be equal to 0.02 pi meters. And we're gonna come back and approximate with pi when we substitute it into our mass equation in our final. All right. So now we have the two values we needed in order to calculate our mass, we can substitute those in and we get our, that our mass M is gonna be equal to 958. kg per meter cubed, multiplied by 0.02 high meters. Cute. The unit of meters cub will divide it. We're gonna be left with just kilograms. And if we work this out on our calculator, we get to the max and it's gonna be about 60. kilogram. If we round this to one decimal place, we compare to our answer choices. We can see that this is gonna correspond with answer choice. C OK. So the mass of the wine is 60.2 kg. Thanks everyone for watching. I hope this video helped see you in the next one.

A 1.0-m-diameter vat of liquid is 2.0 m deep. The pressure at the bottom of the vat is 1.3 atm. What is the mass of the liquid in the vat?

Verified Solution

Key Concepts

Hydrostatic Pressure

Density

Volume of a Cylinder