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. What is the pressure at a depth of $5000m$in the ocean?

B. What is the fractional volume change $∆V/V$ of seawater at this pressure?

C. What is the density of seawater at this pressure?

a. 50 g of gasoline are mixed with 50 g of water. What is the average density of the mixture?b. 50 cm³ of gasoline are mixed with 50 cm³ of water. What is the average density of the mixture?

A U-shaped tube, open to the air on both ends, contains mercury. Water is poured into the left arm until the water column is $10.0cm$ deep. How far upward from its initial position does the mercury in the right arm rise?

Disk brakes, such as those in your car, operate by using pressurized oil to push outward on a piston. The piston, in turn, presses brake pads against a spinning rotor or wheel, as seen in$FIGURECP14.74$ . Consider a $15\mathrm{kg}$ industrial grinding wheel, $26\mathrm{cm}$ in diameter, spinning at $900\mathrm{rpm}$. The brake pads are actuated by $2.0-\mathrm{cm}-$diameter pistons, and they contact the wheel an average distance $12\mathrm{cm}$ from the axis. If the coefficient of kinetic friction between the brake pad and the wheel is $0.60$, what oil pressure is needed to stop the wheel in $5.0s$$5.0\mathrm{s}$ ?

A bucket is filled with water to a height of $23\mathrm{cm}$, then a plug is removed from a $4.0-\mathrm{mm}-diameter$ hole in the bottom of the bucket. As the water begins to pour out of the hole, how fast is it moving$?$