The free surface of oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled by an angle . If the acceleration is a m/s2, what will be the slope of the free surface?
Let us assume the tanker is pulled by a force F and it produces an acceleration in the forward direction. Let m be the mass of a small element. As the tanker is pulled forward and accelerates, the small element also experiences a force in the same direction. The inertia of rest makes the element to remain at rest and hence as the tank moves forward, the element moves backwards as a result of inertia.
Force acting on m, F1 = ma in the backward direction
F2 = mg which is in a vertically downward direction.
The normal reaction gets balanced by various components: from F1
The situation when there is a maximum angle inclination by the surface,
So required slope,
So,