Question #42473

A cylindrical container filled with a liquid of density $\rho_f$ is accelerated vertically upwards with a time-varying acceleration $a(t) = \alpha t$, where $\alpha = 4 \text{ m/s}^3$. A small sphere of mass $m = 1 \text{ kg}$, volume $V$, and density $\rho_s = \rho_f / 2$ is released from rest at the bottom of the container at $t = 0$. The sphere experiences a relative velocity-dependent drag force $F_D = -b v$, where $b = 2 \text{ kg/s}$ and $v$ is the velocity of the sphere relative to the container. Assuming the container is sufficiently tall, what is the work done by the pseudo force on the sphere in the reference frame of the container during the interval $t = 0$ to $t = 1 \text{ s}$? (Take $g = 10 \text{ m/s}^2$)