A solid cube of side length 5.0cm and mass 0.040kg is released from rest while fully submerged in seawater whose density increases linearly with depth according to ρ(y)=ρ0+αy, where y is the depth measured downward from the water surface, ρ0=1.02×103kgm−3, and α=3.0×102kgm−4. At the moment of release the cube is at a depth of 0.80m. Neglect viscous drag.
(a) Express the magnitude of the upward force exerted by the water on the cube in terms of its instantaneous depth y below the surface.
(b) Obtain an algebraic expression for the net force acting on the cube as a function of y during its upward motion, and hence derive the corresponding expression for its acceleration a(y).
(c) Determine the depth yeq (if any) above which the cube’s acceleration would reverse direction. Explain the physical significance of this result.
(d) Using your result from part (b), calculate the cube’s initial acceleration immediately after release.