Physics

Problem

A rectangular block of density

\rho_b

floats in a liquid of density

\rho_{\ell}

with exactly half of its volume submerged when the container is at rest. The container is then given an upward acceleration of magnitude

a

. Derive an expression for the fraction

f

of the block’s volume that is submerged during the acceleration in terms of

\rho_b,\,\rho_{\ell},\,a

, and

g

Intuitive explanation

When the container accelerates upward, the block experiences an effective gravity that's stronger than $g$ alone—think of it like the block is in a more intense gravitational field. The buoyant force and weight must still balance for floating equilibrium, but now both are affected by the effective acceleration $g + a$ . Since the effective gravity increases while the block's density stays fixed, it sinks deeper to displace more liquid and generate more buoyant force. Set up force balance in the accelerating frame to find how the submerged fraction changes.

Intuitive explanation

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