A transparent tank of water rests on the floor of an elevator
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
A transparent tank of water rests on the floor of an elevator. A small rectangular block of wood (density less than that of water) floats at rest on the water surface. The elevator is initially at rest, then begins to move according to the following sequence of motions, each lasting several seconds so that transient sloshing has died out before measurements are made:
• Stage I: constant upward acceleration of magnitude a1.
• Stage II: constant velocity (no acceleration).
• Stage III: constant downward acceleration of magnitude a2.
Assume 0<a2<g and neglect viscosity and surface tension effects.
(a) Qualitatively describe how the pressure at a fixed depth h below the water surface during Stage I compares with the pressure at the same depth during Stage II. Support your answer with reasoning based on forces acting on a fluid element.
(b) During Stage I, does the wooden block float higher, lower, or at the same depth relative to the water surface compared with Stage II? Explain your reasoning.
(c) During Stage III, determine whether the wooden block’s center of mass is closer to or farther from the floor of the elevator than it is during Stage II. Justify your conclusion without using explicit numerical calculations.
(d) Suppose the downward acceleration in Stage III were increased until it exceeded g. Predict what would happen to the block and to the pressure at depth h. Provide a clear explanation connected to forces on both the block and the fluid.