Calculating to mass of a water column above a specific point

In summary, the pressure on the left cap is 1atmosphere, and the pressure on the right cap is 1+d*g*h, for a total of 1.5atmosphere.
  • #1
Emily Chetner
5
0
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Part D. I looked up the answer and input it already, which is why it says correct, but i am beyond stumped. No idea how to do this. I know the pressure at the dotted lines are equal and that pressure=force/area. I also know the pressure at an area is equal to whatever is above it so the pressure on the left arm= 1atmosphere but I am not sure if i would also include the 1kg weight. And I also know the pressure on the right arm is 1atm+ d*g*h and maybe + the kg weight. But I am so stumped on where to go from here
 

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  • #2
Emily Chetner said:
I also know the pressure at an area is equal to whatever is above it so the pressure on the left arm= 1atmosphere but I am not sure if i would also include the 1kg weight. And I also know the pressure on the right arm is 1atm+ d*g*h and maybe + the kg weight.
Yes, you must include all the forces acting on the cap. Do that for both sides and you will get there.
(How did you get the right answer for the first part?)
 
  • #3
haruspex said:
Yes, you must include all the forces acting on the cap. Do that for both sides and you will get there.
(How did you get the right answer for the first part?)

i don't understand how to do this though. How do you add 1atmosphere to the 1kg weight?
 
  • #4
Emily Chetner said:
i don't understand how to do this though. How do you add 1atmosphere to the 1kg weight?
1 atm is a pressure, 1kg is a mass. What force on the cap results from each?
 
  • #5
i honestly have no idea. I've been working on this for at least an hour and have made no progress. If I am supposed to incorporate all forces acting on this cap i don't get how to go that if I am dealing with mass and pressure?
 
  • #6
Emily Chetner said:
i honestly have no idea. I've been working on this for at least an hour and have made no progress. If I am supposed to incorporate all forces acting on this cap i don't get how to go that if I am dealing with mass and pressure?
1. What is the relationship between pressure and force? You must have been given an equation connecting them.

2. Why does placing a mass on top of something result in a force?
 
  • #7
i have Pressure=Force/Area. But that hasnt done me any good this far because I literally have no idea how to do this problem. If i plug in numbers than I have 1atm=1kg/1pi and I have nothing to solve for so I don't know how to use this equation in this context
 
  • #8
Emily Chetner said:
i have Pressure=Force/Area. But that hasnt done me any good this far because I literally have no idea how to do this problem. If i plug in numbers than I have 1atm=1kg/1pi and I have nothing to solve for so I don't know how to use this equation in this context
It is a mistake to plug in numbers at the start. Always try to work symbolically. It makes the ideas clearer, and many other advantages.
You are not told the actual areas, but you are told the ratio between them. The trick is to create a variable, A say, for the smaller area, so the large area is 4A.
Let atmospheric pressure be Pa. Using your formula, what forces does the atmosphere exert on the two caps?

Please try to answer question 2 in my previous post.
 
  • #9
ok, i give up, thanks though
 

1. How do you calculate the mass of a water column above a specific point?

The mass of a water column above a specific point can be calculated by multiplying the density of water (typically 1000 kg/m³) by the volume of water above the point. The volume can be determined by multiplying the cross-sectional area of the column by the height of the water column.

2. What units should be used when calculating the mass of a water column?

The density of water is typically measured in kilograms per cubic meter (kg/m³), so the volume of the water column should be measured in cubic meters (m³) and the resulting mass will be in kilograms (kg).

3. How do you determine the cross-sectional area of a water column?

The cross-sectional area of a water column can be determined by measuring the diameter or radius of the column at the specific point and using the formula for the area of a circle (A = πr² or A = π(d/2)²) to calculate the cross-sectional area.

4. Can the mass of a water column change over time?

Yes, the mass of a water column can change over time as the water moves or evaporates. If there is a change in the water level or temperature, the density of the water may also change, resulting in a different mass for the same water column.

5. Is it necessary to account for the weight of the container or vessel holding the water column?

No, when calculating the mass of a water column, only the mass of the water above the specific point is considered. The weight of the container or vessel is not included as it is not part of the water column itself.

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