Question

Consider a box filled partially with water. The box is accelerated with an acceleration "a". In this way the water is pushed back.
Derive h(x) (see picture below) in function of x, l, a, and g.
My result is h(x)=(al-2gax)/g
Is it correct?

Answer 1

I wrote wrong the equartion in the test above; I meant:
\[h(x)=\frac{ al-2ax }{ g }\]

Answer 2

If you take h to be the difference in height compared to the case of zero acceleration, and take x=0 to be the left hand side of the box, i get h(x)=(l/2 - x)a/g which looks like your answer aside from a factor of 2, probably a different choice of origin ?

Answer 3

When I looked at the question I had no clue what to do with it, then I saw it was a nice example of einstein's equivalence principle : )

Answer 4

ahah what's einstein equivalence principle? you mean inertial mass= weightful mass (I don't know how to translate properly in english)
is that you equation?:
\[h(x)=\frac{ (l/2-x)a }{ g }\]
right?

Answer 5

yes that is my equation - einstein's equivalence principle says that the physics of uniform acceleration is the same as physics in a uniform gravitational field, and it occured to me that the water surface will be perpendicular to the direction of the equivalent gravitational field

Answer 6

the equivalent gravitational acceleration is vector g minus vector a, for this problem

Answer 7

Wow

Answer 8

I'm metabolizing it but i think I've understood

Answer 9

thanks for posting the question, it was fun

Answer 10

you mean that the resulting "fake gravity" vector is