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- Oil having a density of 930 kg/m3 floats on water. A rectangular block of wood 4.00 cm high and with a density of 960 kg/m3 floats partly in the oil and partly in the water. The oil completely covers the block. How far below the interface between the two liquids is the bottom of the block?What fraction of an iceberg floating in the ocean is above sea level? Assume the density of the iceberg is 917 kg/m3.A certain man has a mass of 80 kg and a density of 955 kg/m3 (excluding the air in his lungs). (a) Calculate his volume. (b) Find the buoyant force air exerts on him. (c) What is the ratio of the buoyant force to his weight?
- Gauge pressure in the fluid surrounding an infant's brain may rise as high as 85.0 mm Hg (5 to 12 mm Hg is normal), creating an outward force large enough to make the skull grow abnormally large. (a) Calculate this outward force in newtons on each side of an infant's skull if the effective area of each side is 70.0 cm2. (b) What is the net force acting on the skull?Rank the buoyant forces exerted on the following five objects of equal volume from the largest to the smallest. Assume the objects have been dropped into a swimming pool and allowed to come to mechanical equilibrium. If any buoyant forces are equal, state that in your ranking. (a) a block of solid oak (b) an aluminum block (c) a beach ball made of thin plastic and inflated with air (d) an iron block (e) a thin-walled, sealed bottle of waterA 62.0-kg survivor of a cruise line disaster rests atop a block of Styrofoam insulation, using it as a raft. The Styrofoam has dimensions 2.00 m 2.00 m 0.090 0 m. The bottom 0.024 m of the raft is submerged. (a) Draw a force diagram of the system consisting of the survivor and raft. (b) Write Newtons second law for the system in one dimension, using B for buoyancy, w for the weight of the survivor, and wr for the weight of the raft. (Set a = 0.) (c) Calculate the numeric value for the buoyancy, B. (Seawater has density 1 025 kg/m3.) (d) Using the value of B and the weight w of the survivor, calculate the weight w, of the Styrofoam. (e) What is the density of the Styrofoam? (f) What is the maximum buoyant, force, corresponding to the raft being submerged up to its top surface? (g) What total mass of survivors can the raft support?
- An iron block of volume 0.20 m5 is suspended from a spring scale and immersed in a flask of water. Then the iron block is removed, and an aluminum block of the same volume replaces it. (a) In which case is the buoyant force the greatest, for the iron block or the aluminum block? (b) In which case does the spring scale read the largest value? (c) Use the known densities of these materials to calculate the quantities requested in parts (a) and (b). Are your calculations consistent with your previous answers to parts (a) and (b)?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 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.
- A wooden block floats in water, and a steel object is attached to the bottom of the block by a string as in Figure OQ14.3. 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.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?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.