Pho.rs: Different level

Условие

Русский

A thin tube of cross-sectional area $S$ is bent into a U-shaped vessel. There is a massless piston in its horizontal part and it is connected to the left wall by a spring. There are two immiscible liquids in the vessel: a liquid of density $\rho_1$ in the left limb and a liquid of density $\rho_2 < \rho_1$ in the right limb. In equilibrium, the difference in levels is $\Delta h$ and the spring is undeformed. The stiffness $k$ of the spring is chosen such that when additional liquid of density $\rho_1$ is added to the left limb, the difference in levels $\Delta h$ remains constant.

A1 Determine the stiffness $k$ of the spring.

A volume $\Delta V$ of liquid with density $\rho_2$ is added to the left limb, such that the upper surfaces in the limbs become level.

A2 Determine the volume $\Delta V$ added to the left limb.

The piston is frictionless. The liquid does not leak between the piston and vessel walls, nor does it spill out of the vessel. The volume of the spring can be neglected. The liquids are immiscible and do not flow into the other vertical limb. The acceleration due to gravity is $g$.