QUICK QUIZ 14.1 (end of section 14.2) You have just started taking SCUBA diving lessons in a swimming pool when your friend proposes an easier method that will allow you to breathe while walking on the bottom of your 4-meter-deep pool. He proposes using a long metal pipe as an elongated snorkel and describes how you may breathe through this pipe while standing on the pool bottom, provided that the pipe is long enough to clear the surface of the water. If your friend tries this elongated snorkel, he will a) be able to breathe with little difficulty, b) be able to breathe with moderate difficulty, c) not breathe, and come to the surface gasping for air, or d) impossible to determine until it is actually attempted.

QUICK QUIZ 14.1 ANSWER (c). DO NOT ATTEMPT THIS STUNT! The additional pressure of the water on your chest associated with 4 meters of depth is about 0.4 x 105 Pa, considering about 1 atmosphere increase of pressure for each 10 meters of depth. To simulate this extra pressure, lie down, place a 1200 lb weight on your chest and try to breath. In SCUBA diving, the pressure of the air that you breathe is adjusted through a regulator to the pressure of the surrounding water. The extra pressure associated with as little as a depth of half a meter can be enough to cause difficulty in breathing. For this reason, snorkels are designed to be used with the swimmer in the horizontal position rather than vertical to place the chest as close to the surface of the water as possible.

QUICK QUIZ 14.2 (end of section 14.4) For a physics experiment, you drop three objects of equal mass into a swimming pool. One object is a piece of pine, the second object is a hunk of copper and the third object is a hunk of lead. The relationship between the magnitudes of the buoyant forces on these three objects will be a) Fcopper > Fpine > Flead, b) Fpine > Fcopper > Flead, c) Flead > Fcopper > Fpine or d) Fcopper > Flead > Fpine.

QUICK QUIZ 14.2 ANSWER (b). From Archimedes’ principle, the magnitude of the buoyant force will be equal to the weight of the water displaced. From Table 14.1, lead and copper are more dense than water and will therefore sink, while pine is less dense than water and will therefore float. The buoyant force for the pine must equal the weight, mg, of the pine since these two forces balance. For completely submerged objects, the buoyant force will be equal to the weight of the water displaced, mwg, and will be less for the denser lead, because of its smaller volume, than for the copper. In addition, the mass of the water displaced will be less than the mass of the equal volume of metal displacing it, so that mw < m. Therefore, the buoyant force on each metal is less than the buoyant force on the pine.

QUICK QUIZ 14.3 (end of section 14.4) By swimming with fins, you manage to take a beach ball to the bottom of a pool. Once the beach ball is completely submerged, as you take it deeper, the buoyant force on the beach ball will a) decrease, b) increase, c) remain constant, or d) impossible to determine.

QUICK QUIZ 14.3 ANSWER (a). If the beach ball were to remain at a constant volume, the volume of the water displaced would remain constant as would the buoyant force. However, as one descends, the pressure increases and the volume of the beach ball would also decrease. Therefore, less water would be displaced at depth and the buoyant force would decrease with depth. If you were to release the ball from the bottom of the pool, not only would it accelerate due to the buoyant force but the acceleration would increase as it traveled to the surface.

QUICK QUIZ 14.4 (end of section 14.5) A certain section of a river has its banks restricted by concrete walls, as shown below from an aerial view. In this narrower section of river compared to the wider sections on either side, a) the cross sectional area of the water will be larger and the velocity of the water will be greater, b) the cross sectional area of the water will be smaller and the velocity of the water will be greater, c) the cross sectional area of the water will be larger and the velocity of the water will be less, d) the cross sectional area of the water will be smaller and the velocity of the water will be less, or e) the cross sectional area of the water will be the same and the velocity of the water will be the same.

QUICK QUIZ 14.4 ANSWER (b). From the equation of continuity, Equation 14.7, Av = constant for each section of the river. Since the level of the water will not increase significantly for the narrow section (unless the velocity of the water is extreme), the smaller width of that section implies a smaller cross sectional area and a consequent greater velocity.

QUICK QUIZ 14.5 (end of section 14.5) You would like to change the opening on the nozzle of a fire hose so that the water exiting the hose can reach a height that is four times the present maximum height the water can reach. To do this, you should decrease the cross sectional area of the opening by a factor of a) 16, b) 8, c) 4 or d) 2.

QUICK QUIZ 14.5 ANSWER (d). From the continuity equation, the velocity of the water exiting the hose is inversely proportional to the cross sectional area or v  1/A. However, the kinetic energy of the water that exits the hose will be equal to the potential energy of the water at its maximum height (when you point the hose straight up), or So to increase the height by a factor of four, you must decrease the area by a factor of 2.