Simple fluids but is the application correct

[phyeinstein_c]

Homework Statement

problem states that ... there is a u tube and filled with liquid of densities ρ and 2ρ. the base length of the tube is 'l'. now it is accelerated towards right with accl.=a. if the HEIGHT DIFFERENCE AFTER ACCELERATING THE SYSTEM IS '0'. then what was the height difference before acceleration??

Homework Equations

P=ρgh; F=ma ; F=(ρ.V)a ;

The Attempt at a Solution

i tried to find pressure at bottom most level at interface of the two liquids, then the net force, then applied Newtons 2nd law, but could'nt get the solution...

 

[tiny-tim]

hi phyeinstein_c!

hint: what will be the angle of the surface of the fluid (in either half of the 'U') ?

 

[ashishsinghal]

lets see...if the u tube is moving towards right the major driving force is on the left side of the tube. since the heights are equal the 2p liquid is in the left tube .

first find relations between height h1 and h2 in the two sides of tube when at rest...then find height h when accelerated.. then keeping volume constant use h1 + h2 = 2h

 

[phyeinstein_c]

hi phyeinstein_c!

hint: what will be the angle of the surface of the fluid (in either half of the 'U') ?

they're not at angle. initially they are at a height difference. that's it is wat is given.

 

[tiny-tim]

i know, i mean, suppose there was only one pipe (or a jar or vase), what would be the angle of the water surface?

 

[phyeinstein_c]

it wud be horizontal obviously

 

[tiny-tim]

nope!

 

[phyeinstein_c]

why...?

 

[tiny-tim]

suppose the water was ice, and the surface was at an angle, and a drop of water was on the surface …

what angle would the surface have to be for the drop of water to stay where it is?

 

[phyeinstein_c]

<=45 i guess

 

[tiny-tim]

<=45 i guess

how do you get that?

 

[phyeinstein_c]

:P just guessing... mgsinθ is equal to the friction acting.. of surface tension watever... unless u describe the surface of ice to be smooth...

 

[tiny-tim]

… unless u describe the surface of ice to be smooth...

yes, of course it's smooth!

 

[phyeinstein_c]

ok... then it can't stay where it is..

 

[tiny-tim]

why not?

(if the block of ice is accelerating)

 

[phyeinstein_c]

oh yeah that's there... true.. then we can find the component of ma and normal reaction in horizontal direction and solve..