A large open-top tank that is half-filled with water is rigidly mounted on a rail cart
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
A large open-top tank that is half-filled with water is rigidly mounted on a rail cart. The cart starts from rest and accelerates horizontally with constant magnitude 3.0ms−2 along a straight track. A small lightweight cube of negligible mass compared to the displaced water floats gently on the water surface throughout the motion. Assume the water remains in static equilibrium relative to the accelerating cart once transients have died out.
(a) With respect to the cart, the free surface of the water tilts by an angle θ relative to the horizontal. Derive an expression for θ in terms of given quantities, then calculate its numerical value.
(b) Determine the horizontal component of the water pressure gradient inside the tank. Express your answer as a function of depth below the tilted surface.
(c) Will the cube drift toward the front wall, the back wall, or remain directly beneath its initial position relative to the cart? Explain your answer using the pressure distribution found in part (b).
(d) After the cart reaches its cruising speed and the acceleration drops to zero, describe qualitatively how the water surface and the position of the cube evolve with time until a new equilibrium is reached.