U-Tube Mass and Pressure Problem

AI Thread Summary
The discussion revolves around a U-tube filled with water, where one arm has twice the radius of the other, and both arms are capped. Participants are trying to determine the mass of water in the right arm between a specified water level and the cap. Key questions include the units of pressure, the water pressure at the surface of both tubes, and the pressure difference at the level line in the right tube. There is a 1 kg weight on top of each tube, which adds complexity to the pressure calculations. The thread highlights the need for participants to engage more deeply with the problem rather than seeking direct answers.
dspivak01
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1. A U-tube is filled with water, and the two arms are capped. (Intro 1 figure) The tube is cylindrical, and the right arm has twice the radius of the left arm. The caps have negligible mass, are watertight, and can freely slide up and down the tube.



2. The locations of the two caps at equilibrium are now as given in this figure. (Part D figure) The dashed line represents the level of the water in the left arm.
What is the mass of the water located in the right arm between the dashed line and the right cap?



3. Not a clue of how to start (or finish) this problem
 

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dspivak01 said:
1. A U-tube is filled with water, and the two arms are capped. (Intro 1 figure) The tube is cylindrical, and the right arm has twice the radius of the left arm. The caps have negligible mass, are watertight, and can freely slide up and down the tube.



2. The locations of the two caps at equilibrium are now as given in this figure. (Part D figure) The dashed line represents the level of the water in the left arm.
What is the mass of the water located in the right arm between the dashed line and the right cap?



3. Not a clue of how to start (or finish) this problem

What are the units of pressure? What is the water pressure at the surface in the left tube? What is the pressure at the surface in the right tube? What is the pressure at the level line in the right tube? What accounts for the difference between the pressure at the surface in the right tube, and the level line in the right tube?
 
Everything i put up is all that i know. The radius of the right side is double of the left side. and there is a 1kg weight on top of each tube like in the attached picture.
 
dspivak01 said:
Everything i put up is all that i know. The radius of the right side is double of the left side. and there is a 1kg weight on top of each tube like in the attached picture.

Sorry, that is not enough effort on your part for this website. We do not do your work for you here.

Please answer my questions in my post above. You might actually solve your own schoolwork question by doing so.
 
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Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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