Why Does the Surface of a Liquid Slope When the Container is Accelerated?

[andyrk]

Homework Statement

When a vessel containing a liquid is accelerated as shown in the attachment its surface slopes as shown, making an angle θ with the horizontal. Does this happen?

Homework Equations

Consider a differential mass element inside the liquid.
It experiences forces F₁ and F₂ in the right and the left direction respectively. Let its two sides have area A and be at depths h₁ and h₂ beneath the water surface. Then if we need to prove that why does the surface slope it is sufficient to prove that h₁>h₂ (This can only happen if the surface is sloped so that the distance from the water surface is not the same)
So :

F₁ > F₂ (As the differential element accelerates in the x direction the right side force has to be greater that the left side force)
=>F₁/A > F₂/A
=>P₁>P₂ (P₁ and P₂ are the pressures at the left and the right side of the differential element respectively)
=>h₁ρg>h₂ρg
=>h₁>h₂




My doubt was that what are the causes of F₁ and F₂?

Is it because of the cohesive forces? But aren't those forces attractive? So should the directions of the two forces F₁ and F₂ be opposite? So would that mean that the differential molecule is being pulled outside to expand? Really weird I know, but what causes both the forces?

 

[voko]

It is easiest to consider the accelerated frame and find the net force on the liquid in that frame. The level of a liquid, in steady state, is always perpendicular to the direction of the force.