- #1

ValeForce46

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- 3

- Homework Statement
- A tube of mass ##M= 18 kg ##, section ##A= 300 cm^2 ## and lenght ##l= 200 cm ## is sealed to the top and opened to the bottom. Initially the tube contains only air at a pressure ##p_0= 1 bar ##, occupying the whole volume ##A*l ## (see picture a). Then, the tube is leaning on a surface of alcol (density ##ρ=0.8 g/cm3 ##) and, keeping the tube vertically, it is immersed until it reaches a position of balance. In this process the air inside the tube is compressed (see picture b).

In conditions of equilibrium, calculate:

a)the pressure ##p ## of the air inside the tube;

b)the difference of level ##d ## between the surface of the alcol inside and outside the tube;

c)the length ##b ## of the tube which emerges.

- Relevant Equations
- Stevino's Law ##p=p_0+ρ*g*h ##

Force caused by pressure ##F=p*A##

This is a problem from a past exam.

For point a)

the balance between force should be given by the following equation

$$M*g+p_0*A=ρ*g*(A*d)+p*A$$

But I still have two unknown values...

I know that pressure outside the tube at depth d is

$$p(d)=p_0+ρ*g*d$$

and this has to be equal to the pressure at depth d inside the tube, because that's a free surface.

What do I do now? Is the equation of the balance of the forces correct?

For point a)

the balance between force should be given by the following equation

$$M*g+p_0*A=ρ*g*(A*d)+p*A$$

But I still have two unknown values...

I know that pressure outside the tube at depth d is

$$p(d)=p_0+ρ*g*d$$

and this has to be equal to the pressure at depth d inside the tube, because that's a free surface.

What do I do now? Is the equation of the balance of the forces correct?