Chapter 14: Fluids and Elasticity

A 1.0-m-diameter vat of liquid is 2.0 m deep. The pressure at the bottom of the vat is 1.3 atm. What is the mass of the liquid in the vat?

In FIGURE Q14.5, is p_A larger than, smaller than, or equal to p_B? Explain

A cylinder with cross-section area $A$floats with its long axis vertical in a liquid of density $\rho$.

a. Pressing down on the cylinder pushes it deeper into the liquid. Find an expression for the force needed to push the cylinder distance $x$deeper into the liquid and hold it there.

b. A $4.0-cm$-diameter cylinder floats in water. How much work must be done to push the cylinder $10cm$deeper into the water?

A less-dense liquid of density ${\rho }_1$floats on top of a more-dense liquid of density ${\rho }_2$. A uniform cylinder of length $L$and density ${\rho }_{}$, with ${\rho }_1<\rho <{\rho }_2$, floats at the interface with its long axis vertical. What fraction of the length is in the more-dense liquid?

A $30cm$-tall, $4.0cm$-diameter plastic tube has a sealed bottom. $250g$of lead pellets are poured into the bottom of the tube, whose mass is $30g$, then the tube is lowered into a liquid. The tube floats with$5.0cm$ extending above the surface. What is the density of the liquid?

One day when you come into physics lab you find several plastic hemispheres floating like boats in a tank of fresh water. Each lab group is challenged to determine the heaviest rock that can be placed in the bottom of a plastic boat without sinking it. You get one try. Sinking the boat gets you no points, and the maximum number of points goes to the group that can place the heaviest rock without sinking. You begin by measuring one of the hemispheres, finding that it has a mass $21g$and a diameter of $8.0cm$. What is the mass of the heaviest rock that, in perfectly still water, won't sink the plastic boat?

A spring with spring constant 35 N/m is attached to the ceiling, and a 5.0-cm-diameter, 1.0 kg metal cylinder is attached to its lower end. The cylinder is held so that the spring is neither stretched nor compressed, then a tank of water is placed underneath with the surface of the water just touching the bottom of the cylinder. When released, the cylinder will oscillate a few times but, damped by the water, quickly reach an equilibrium position. When in equilibrium, what length of the cylinder is submerged?

A plastic "boat" with a $25{\mathrm{cm}}^2$square cross section floats in a liquid. One by one, you place $50g$masses inside the boat and measure how far the boat extends below the surface. Your data are as follows:

Draw an appropriate graph of the data and, from the slope and intercept of the best-fit line, determine the mass of the boat and the density of the liquid.

A$355\mathrm{mL}$soda can is $6.2\mathrm{cm}$in diameter and has a mass of $20g$. Such a soda can half full of water is floating upright in water. What length of the can is above the water level?

A nuclear power plant draws $3.0\times {10}^6\mathrm{L}/\min$ of cooling water from the ocean. If the water is drawn in through two parallel,$3.0-\mathrm{m}$-diameter pipes, what is the water speed in each pipe?