19. Fluid Mechanics

A common effect of surface tension is the ability of a liquid to rise up a narrow tube due to capillary action. Show that for a narrow tube of radius r placed in a liquid of density ρ and surface tension γ, the liquid in the tube will reach a height h = 2γ/ρgr above the level of the liquid outside the tube, where g is the gravitational acceleration. Assume that the liquid “wets” the tube and that the liquid surface is vertical at the contact with the inside of the tube.

Which statement best explains the reason some insects can walk across the surface of a lake?

A helium balloon of volume $V$ is fully submerged in air of density ${\rho }_{\mathrm{air}}$ under standard atmospheric pressure. What is the magnitude of the buoyant force $F_b$ acting on the balloon?

Which of the following determines an object's ability to float in water?

Will the same ship float higher in $\mathrm{salt} \mathrm{water}$ than in $\mathrm{freshwater}$? Choose the best explanation.

According to Archimedes' principle, if the buoyancy of an object is positive, it will: $F\_b>0$

Why does a small pebble sink in water?

When an object is completely submerged in water, how does its $V\_\mathrm{object}$ compare to the $V\_\mathrm{displaced}$ of water?

When a piece of ice floats in water, what fraction of its volume remains above the water surface?

Why can some insects walk on water?

Why does hot air rise and cold air sink in Earth's atmosphere?

To ensure that a ship is in stable equilibrium, would it be better if its center of buoyancy was above, below, or at the same point as its center of gravity? Explain.

In the context of buoyancy, does the volume of an object alone determine whether it will float or sink in a fluid?

Which principle explains why certain insects can walk on water?

In a container of water, what typically happens to hot water compared to cold water, and why?