a) the object's density. c) the submerged volume of the object. b) the mass of the object. d) the shape of the object.

Transcription

1 Multiple Choice Questions ( Buoyant force and floatability) 1. The buoyant force on an object is dependent on a) the object's density. c) the submerged volume of the object. b) the mass of the object. d) the shape of the object. 2. The buoyant force on an object submerged in a fluid depends on a) the object's density. d) (a) and (b) but not (c). b) the fluid's density. e) (b) and (c) but not (a). c) the acceleration due to gravity. 3. The property that most determines whether or not an object will float in oil is the object's a) weight. c) density. b) mass. d) volume. 4. An object is placed in a fluid. The buoyant force on the object is proportional to (careful!!) a) the density of the object. d) (b) and (c) but not (a). b) the volume of the object. e) (a) and (b) and (c). c) the density of the fluid. 6. Why does a duck float? (This is a real question, not a joke!) a) The duck weighs less than water. c) The duck has feathers b) The duck can swim. d) The duck has a smaller density than water. 7. An object can float provided its is than the of the fluid, a) mass...less... mass c) mass...greater...density b) density... less... density d) density... less... mass 8. A wooden boat with a density of 0.48 g/cc is floating in a vat of oil whose density is 0.80 g/cc. What percentage of the boat is floating above the surface of the oil? a) 42 % c) 52 % b) 60 % d) 40 %

2 9. Oil has a smaller density than water. Therefore, an object that will float in oil will a) float in water, with more of the object submerged. b) float in water, with the same amount of the object submerged. c) float in water, with less of the object submerged. d) not float in water. e) There is not enough information. 10. A boat with a density of 0.75 g/cc is floating in water. What percentage of the boat is floating above the surface of the water? a) 25 % c) 75 % b) 50 % d) None; the boat will actually sink! 11. The pressure at an underwater depth of 33.7 feet is 2 atmospheres (atm). At what depth would the pressure be 3 atm? a) 67.4 feet. c) feet d) feet. d) The pressure can never reach 3 atm. 12. The pressure at an underwater depth of 33.7 feet is 2 atmospheres (atm). At what depth would the pressure be 4 atmospheres? a) 67.4 feet c) feet b) feet d) the pressure can never reach 4 atm Which has a greater buoyant force acting on it, a floating 100 g piece of wood, or a floating 50 g piece of wood? a) The 100 g piece of wood. b) The 50 g piece of wood. c) Since both pieces of wood are floating, they experience the same buoyant force. d) There is not enough information. Floatability Questions 1. - Calculate the buoyant force, the density and volume of a body. We know that its weight in air is 7 N and immersed in water, 5.5 N. Data: g =9,8 m/s 2 Sol: F b = 1,5 N; V = 1, m 3 ; d = 4668,5 kg/m A bargain hunter purchases a "gold" crown at a flea market. After she gets home, she hangs it from a scale and finds its weight in air to be 7.84 N. She then weighs the crown while it is immersed in water (density of water is 1000 kg/m 3 ) and now the scale reads 6.86 N. Is the crown made of pure gold if the density of gold is 19.3 x 10 3 kg/m 3? Sol: 8000 kg /m 3 < kg /m 3 ; No. This is not gold!!

3 3. - Complete the table: Iron Aluminum Wood (pine tree) Density (kg/m 3 ) Mass (kg) Volume (m 3 ) Weight (in air) Weight (in water) Bouyant force 4. - Complete the table: Cupper Platinum Wood (oak tree) Density (kg/m 3 ) Mass (kg) Volume (m 3 ) Weight (in air) Weight (in water) Bouyant force 5. - Complete the table and indicate in what cases the objects will float in water. Solid Mass (kg) Volume (m 3 ) Density Will it float? A 450 0,5 B 700 0,1 C A ship sailing from the ocean (salt-water) into a fresh-water harbor sinks slightly deeper into the water. Does the buoyant force on the ship change? Why or why not? If so, does the buoyant force increase or decrease? If not, why does the ship sail lower in the water? 7. - An iceberg has a total volume of 100 m 3. Find the volume of the submerged part. Data: d (ice) = 900 kg / m 3 d (seawater) = 1030 kg / m 3 Pressure: Basic Principle of Hidrostatics and Pascal 8. - One piece of metal is parallelepiped-shaped, with dimensions 30x40x55 cm and density 6500 kg / m³. Calculate the pressure exerted by each one of their faces. 9 - Wind exerts a pressure of 6.10 ⁵ Pa. Calculate the force on a wall of a house (10x12) m dimensions A water bed is 2.0 m on sides an 30 cm deep. a) Find its weight if the density of water is 1000 kg/m 3. Sol: N b) Find the pressure the water bed exerts on the floor. Assume that the entire lower surface of the bed makes contact with the floor. Sol: 2940 Pa

4 11. - What pressure supports a submerged scuba diver at 60 m depth in seawater? If he wants to uncover a can with an area of 10 cm 2 at that depth, what force will have to make? Data: d = 1030 kg / m 3, g = 9.8 m / s 2. Sol: P = N/m 2 ; F = 605,64 N 12.- a) Calculate the absolute pressure at an ocean depth of 1000 m. Assume that the density of water is 1000 kg/m 3 and that P atm = 1.01 x 10 5 Pa (N/m 2 ). Sol: 9, N/m 2 (Pa) b) Calculate the total force exerted on the outside of a 30.0 cm 2 diameter circular submarine window at this depth. Sol: 69,27 N 13 - A man of m = 70 kg is standing on a square area of 0,2 m 2 side. If he takes a weight of 35 kg, calculate what the new surface to be measured so that the pressure is the same. Sol: 0,3m Calculate the pressure exerted on the bag s ground of 50 kg whose dimensions are 1 m long, 1 m wide and 0.5 m high. Data: g =9,8 m/s 2 a) When it rests on the side of the largest surface. Sol: P = 490 N/m 2 b) When it rests on the side of lowest surface. Sol: P = 980 N/m The patient in figure below is to receive an intravenous injection of medication must be 109 kpa at the injection point. If the fluid has a density of 1020 kg/m 3 find the height at which the bag of fluid must be suspended above the patient. Assume that the pressure inside the bag is one atmosphere. Sol: 0,770 m Calculate the hydrostatic difference in blood pressure between the brain and the foot in a person of height 1.83 m. The density of blood is 1.06 x 10 3 kg/m 3. Sol: 1, Pa Calculate the difference in pressure between two points in a swimming pool, 3 m apart in same vertical. Sol: Pa A submarine has a 50 cm circular radio hatch. Calculate the pressure and force exerted on it at 300 m depth, if the density is 1030 kg / m³. Sol: P = 3, Pa; F = 2, N A cylindrical drum of r = 55 cm and h = 120 cm is filled with oil (d = 780 kg / m³). Calculate the pressure and force that supports the base of the container. Sol. P = 917,28 Pa; F= 871,7 N In a pool of 2.5 meters depth there is a circular bottom lid, r = 10 cm. Calculate force to be made to open the lid. According to that force what mass would you be able to lift up on the surface of the Earth? Sol: 769,7 N; F = 78,54 Kg

5 21. - Determine the pressure at the bottom of a container of 250 cm in depth filled with mercury (d = kg / m³). How deep should have a water-filled container to exert equal pressure? Sol: P = 3, Pa; h = 3,4 m The density of olive oil is 780 kg / m³. If we make the experience Torricelli with oil instead of mercury, what height of oil column will be reached that pressure is the same as a column of mercury 760 mm? Sol: 13,26 m A sphere of radius two meters and kg mass is introduced into a liquid whose density is g / ml. Calculate if it floats or sinks, if it sinks, calculate the apparent weight. If it floats calculate the % of submerged volume. Sol: 85% In a U-shaped tube with two open arms water is added by the left arm. Then oil ( d = 920 kg/m 3 ) is added in the right arm. Indicate true or false: a) Water reaches the same height in both arms? b) Do water and oil reach the same height? c) If the height of the oil column is 10 cm, which is the height to reach the water? Sol: 9,2 cm A U-shaped tube of uniform cross section is open to the atmosphere, is partially filled with mercury, then water was poured on each side. If the system is in equilibrium as shown in the figure and h 3 = 2.5 cm calculate the value of h 1. Sol: h 1 = 31,5 cm A U-shaped tube open to the air at both ends contains some mercury. A quantity of water is carefully poured into the left arm of the U-shaped tube until the vertical height of the water column is 15cm. (a) What is the gauge pressure at the water-mercury interface? Sol: 1470 Pa (b) Calculate the vertical distance h from the top of the mercury in the right-hand arm of the tube to the top of the water in the left-hand arm. Sol: h = 13,9 cm

6 27.- To suck lemonade of density 1000 kg/m 3 up a straw to a maximum height of 4.0 cm, what minimum gauge pressure (in atmospheres) must you produce in your lungs? Sol: 3, atm Hydraulic Machines A hydraulic press has two pistons of sections 1500 and 50 cm ². If we apply the smaller one a force of 30 N, calculate the weight we can lift with the other one Determine the section of small piston of a hydraulic press if the biggest piston is 500 cm² and applying a force of 50 N a body of m = 100 kg is lifted A hydraulic press has a piston radii 20 and 120 cm 2. How strong will to do on the small piston so that a mass of 400 kg can be lifted? Johnny the auto mechanic is raising a 1200 kg car on her hydraulic lift so that she can work underneath. If the area of the input piston is 12 cm 2, while the output piston has an area of 700 cm 2, what force must be exerted on the input piston to lift the car? Marc favorite ride at Busch Gardens is the Flying Umbrella, which is lifted by a hydraulic jack. The operator activates the ride by applying a force of 72N to a 30 cm 2 cylindrical piston, which holds the 20,000N ride off the ground. What is the area of the piston that holds the ride? Mr. Sharlow is raising a 2000kg car on his hydraulic lift. If the area of the input piston is 9 cm 2, while the area of the output piston is 630 cm 2, what force must be exerted on the input piston to lift the car?