A 7.05-m radius air balloon loaded with passengers and ballast is floating at a fixed altitude. Determine how much weight (ballast) must be dropped overboard to make the balloon rise 116 m in 17.0 s. Assume a constant value of 1.2 kg/m³ for the density of air. Ballast is weight of negligible volume that can be dropped overboard to make the balloon rise. × What is the buoyant force before and after the ballast is dropped? What is the net force acting on the balloon when it is rising? N Additional Materials Reading

A wooden block floats in water, and a steel object is attached to the bottom of the block by a string as in Figure OQ15.1. If the block remains floating, which of the following statements are valid? (Choose all correct statements.) (a) The buoyant force on the steel object is equal to its weight. (b) The buoyant force on the block is equal to its weight. (c) The tension in the string is equal to the weight of the steel object. (d) The tension in the string is less than the weight of the steel object. (e) The buoyant force on the block is equal to the volume of water it displaces.

What is the greatest average speed of blood flow at 37° C in an artery of radius 2.00 mm if the flow is to remain laminar? What is the corresponding flow rate? Take the density of blood to be 1025 kg/m3.

Liquid toxic waste with a density of 1752 kg/m3 is flowing through a section of pipe with a radius of 0.312 m at a velocity of 1.64 m/s. a. What is the velocity of the waste after it goes through a constriction and enters a second section of pipe with a radius of 0.222 m? b. If the waste is under a pressure of 850,000 Pa in the first section of pipe, what is the pressure in the second (constricted) section of pipe?

Gasoline is piped underground from refineries to major users. The flow rate is 3.00102 m3/s (about 500 gal/ min), the viscosity of gasoline is 1.00103 (N/m2) s, and its density is 680 kg/m3. (a) What minimum diameter must the pipe have if the Reynolds number is to be less than 2000? (b) What pressure difference must be maintained along each kilometer of the pipe to maintain this flow rate?

A 1.00-kg beaker containing 2.00 kg of oil (density = 916.0 kg/m3) rests on a scale. A 2.00-kg block of iron suspended from a spring scale is completely submerged in the oil as shown in Figure P15.63. Determine the equilibrium readings of both scales. Figure P15.63 Problems 63 and 64.

Figure P15.52 shows a Venturi meter, which may be used to measure the speed of a fluid. It consists of a Venturi tube through which the fluid moves and a manometer used to measure the pressure difference between regions 1 and 2. The fluid of density tube moves from left to right in the Venturi tube. Its speed in region 1 is v1, and its speed in region 2 is v2. The necks cross-sectional area is A2, and the cross-sectional area of the rest of the tube is A1. The manometer contains a fluid of density mano. a. Do you expect the fluid to be higher on the left side or the right side of the manometer? b. The speed v2 of the fluid in the neck comes from measuring the difference between the heights (yR yL) of the fluid on the two sides of manometer. Derive an expression for v2 in terms of (yR yL), A1, A2, tube, and mano. FIGURE P15.52

(a) What is the fluid speed in a fire hose with a 9.00-cm diameter carrying 80.0 L of water per second? (b) What is the flow rate in cubic meters per second? (c) Would your answers be different if salt water replaced the fresh water in the fire hose?

Calculate the Reynolds numbers for the flow of water through (a) a nozzle with a radius of 0.250 cm and (b) a garden hose with a radius of 0.900 cm, when the nozzle is attached to the hose. The flow rate through hose and nozzle is 0.500 us. Can the flow in either possibly be laminar?

A man of mass m = 70.0 kg and having a density of = 1 050 kg/m3 (while holding his breath) is completely submerged in water, (a) Write Newtons second law for this situation in terms of the mans mass m, the density of water , his volume V, and g. Neglect any viscous drag of the water, (b) Substitute m = V into Newtons second law and solve for the acceleration a, canceling common factors, (c) Calculate the numeric value of the mans acceleration, (d) How long does it take the man to sink 8.00 m to the bottom of the lake?