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A container filled with fluid is accelerating initially with a1 and instantly changes to a2 (a2 < a1). What would happen to the fluid in the container.

My thoughts on this - If the velocity of the system is v1 when the acceleration changes to a2. The fluid will, at that instant, have a velocity of v1 while container accelerates (with an accleration a2) to v2 (v2>v1) The fluid in the container is moving backwards relative to the container. So, it would splash against the back wall of the container. Is this logically accurate or am I missing something.

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1 Answer 1

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The container will not suddenly accelerate to $v_2$. When you suddenly change the acceleration to $a_2$, you are not providing an impulse to the container, so the velocity of the container just after the change will still be $v_1$ and not suddenly accelerate to $v_2$.

The velocity of the container will increase now too but by rate $a_2$ and not $a_1$(Note that it was increasing before the change too, due to acceleration $a_1$, in case you missed that). The water in the container will also accelerate by $a_2$, and you you won't experience a sudden splash effect.

What would happen to the water is that it will oscillate periodically about an equilibrium position (infinitely if there is no damping). The equilibrium position of water level in an accelerated container is shown by this image:-

enter image description here

When you change from $a_1$ to $a_2$, the equilibrium position changes its inclination $\theta$, so the fluid level starts oscillating about this level.

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Thanks for the lucid explanation. But would the fluid in the container also accelerate with a2 along with the container or move with a velocity v1 (because of inertia) . I'm trying to draw an analogy with a moving vehicle. When a car is stopped by rapid application of brakes, any object inside the car and not rigidly attached to it would be tossed forward because of its inertia. I realise that the car is an example of deceleration whereas the fluid problem is not. I'm trying to understand what role inertia will play in the problem. –  Ryuu Agamaki Sep 4 '13 at 16:56
    
If you decrease acceleration(or provide negative acceleration), the inclination of the equilibrium position $\theta$ decreases, so the water level will also try to increase its inclination. In effect, it will look like the water is lunging forward, and splashing into the forward wall. That's basically what inertia predicts. –  udiboy1209 Sep 4 '13 at 17:03
    
I usually refrain from using the concept of inertia to explain stuff. One would rather use forces(and equilibrium conditions). With inertia, it becomes difficult to talk about non-rigid bodies(like water). –  udiboy1209 Sep 4 '13 at 17:05

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