A cubical block of wood measuring 0.20m on each edge has a mass of 3.0kg. It is floating in water. A block of lead of the same mass (3.0kg) is placed on top of the wood. To what depth "d" does the wood float?

In an immersion measurement of a woman's density, she is found to have a mass of 62.0 kg in air and an apparent mass of 0.0850 kg when completely submerged with lungs empty. (a) What mass of water does she displace? (b) What is her volume? (c) Calculate her density. (d) If her lung capacity is 1.75 L is she able to float without treading water with her lungs filled with air?

A hollow copper (Cu = 8.92 103 kg/m3) spherical shell of mass m = 0.950 kg floats on water with its entire volume below the surface. a. What is the radius of the sphere? b. What is the thickness of the shell wall?

The spirit-in-glass thermometer, invented in Florence, Italy, around 1654, consists of a tube of liquid (the spirit) containing a number of submerged glass spheres with slightly different masses (Fig. P14.41). At sufficiently low temperatures, all the spheres float, but as the temperature rises, the spheres sink one after another. The device is a crude but interesting tool for measuring temperature. Suppose the tube is filled with ethyl alcohol, whose density is 0.789 45 g/cm3 at 20.0C and decreases to 0.780 97 g/cm3 at 30.0C. (a) Assuming that one of the spheres has a radius of 1.000 cm and is in equilibrium halfway up the tube at 20.0C, determine its mass. (b) When the temperature increases to 30.0C, what mass must a second sphere of the same radius have to be in equilibrium at the halfway point? (c) At 30.0C, the first sphere has fallen to the bottom of the tube. What upward force does the bottom of the tube exert on this sphere? Figure P14.41

(a) How high will water rise in a glass capillary tube with a 0.500-mm radius? (b) How much gravitational potential energy does the water gain? (c) Discuss possible sources of this energy.

A host pours the remnants of several of wine into a jug a party. The host then inserts a cork with a 2.00-cm diameter into the bottle, placing it in direct contact with the wine. The host is amazed when the host pounds the cork into place and the bottom of the jug (with a 14.0-cm diameter) breaks away. Calculate the extra force exerted against the bottom if he pounded the cork with a 120-N force.

You are applying for a position with a sea rescue unit and are taking the qualifying exam. One question on the exam is about the use of a diving bell. The diving bell is in the shape of a cylinder with a vertical length of L = 2.50 m. It is closed at the upper circular end and open at the lower circular end. The hell is lowered from air into seawater ( = 1.025 g/cm3) and kept in its upright orientation as it is lowered. The air in the bell is initially at temperature Ti = 20.0C. The bell, with two humans inside, is lowered to a depth (measured to the bottom of the bell) of 27.0 fathoms, or h = 49.4 m. At this depth the water temperature is Tf = 4.0C, and the bell is in thermal equilibrium with the water. The exam question asks you to compare two situations: (i) No additional gas is added to the interior of the bell as it is submerged. Therefore, water enters the open bottom of the bell and the volume of the enclosed air decreases. (ii) The bell is fitted with pressurized air tanks, which deliver high-pressure air into the interior of the bell to keep the level of water at the bottom edge of the bell. This choice requires money and effort to attach the tanks. The exam question asks: Which scenario is better?

A U-tube open at both ends is partially filled with water (Fig. P15.67a). Oil having a density 750 kg/m3 is then poured into the right arm and forms a column L = 5.00 cm high (Fig. P15.67b). (a) Determine the difference h in the heights of the two liquid surfaces. (b) The right arm is then shielded from any air motion while air is blown across the top of the left arm until the surfaces of the two liquids are at the same height (Fig. P15.67c). Determine the speed of the air being blown across the left arm. Take the density of air as constant at 1.20 kg/m3.

The gravitational force exerted on a solid object is 5.00 N. When the object is suspended from a spring scale and submerged in water, the scale reads 3.50 N (Fig. P15.24). Find the density of the object. Figure P15.24 Problems 24 and 25.

A fluid flows through a horizontal pipe that widens, making a 45 angle with the y axis (Fig. P15.48). The thin part of the pipe has radius R, and the fluids speed in the thin part of the pipe is v0. The origin of the coordinate system is at the point where the pipe begins to widen. The pipes cross section is circular. a. Find an expression for the speed v(x) of the fluid as a function of position for x 0 b. Plot your result: v(x) versus x. FIGURE P15.48 (a) The continuity equation (Eq. 15.21) relates the cross-sectional area to the speed of the fluid traveling through the pipe. A0v0 = A(x)v(x) v(x)=A0v0A(x) The cross sectional area is the area of a circle whose radius is y(x). The widening pan of the pipe is a straight line with slope of 1 and intercept y(0) = R. y(x) = mx + b = x + R A(x) = [y(x)]2 = (x + R)2 Plug this into the formula for the velocity. Plug this into the formula for the velocity. v(x)=A0v0(x+R)2