Archimedes. F b (Buoyant Force) DEMO. Identical Size Boxes Which has larger F B. Which is heavier. styrofoam (1 cm 3 ) steel ( 1 cm 3 )

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1 Fluids Density 1

2 F b (Buoyant Force) DEMO Archimedes Identical Size Boxes Which has larger F B Which is heavier styrofoam (1 cm 3 ) steel ( 1 cm 3 ) steel ( 1 cm 3 ) styrofoam (1 cm 3 ) 2

3 Finding the Weight of a Fluid Floating special case 3

4 Key densities Air 1.29 Fresh water 1000 kg/m 3 Sea water 1025 Specific Gravity 4

5 Pressure Ex: 2m 100 kg, cube on floor. 2m 2m 5

6 Pressure at a random location in a static fluid Tank of water Pressure Here? Gauge 6

7 Absolute Pressure Submarine Window 7

8 glass bucket pool * only for static fluids 8

9 Pressure is exerted equally in all directions at a given spot The cause of this pressure is gravity Why? imagine a container of sand in space There would be no pressure anywhere since no force pushing anything (ignoring gravity of sand particles themselves) Bring this sand to the earth Magically vanish the container The sand would move sideways to form a pile The sideways push on the bottom of the pile is the largest due to all the sand above it bearing down Put the sand back into the container The sand still is pushed sideways but the sides of the container push back on it to provide the horizontal forces causing the horizontal pressure forces at each location. A force also comes upwards due to the reaction of the base of the container pushing upwards. The force causing all of these left right up and down force at a given spot comes from the same thing: the vertical pull of gravity 9

10 1.) A 10 m high water storage tank is at an elevation of 20 m above the town below and has water to a depth of 5 m inside. i) Determine the water pressure at a closed faucet on ground level. ii) If the 500 m 3 tank was empty, what power pump, located in the town would be needed to fill the tank in 10 minutes. 10

11 Pascals Principle (Hydraulics) Result Tradeoff * (finding "d" = work=work) 11

12 2.) A piston, A, has a diameter of 0.77 cm, as in the figure. A second piston, B, has a diameter of 4.6 cm. In the absence of friction, determine the force, F, necessary to support the N weight. 12

13 3.) A hydraulic brake system is shown in the Figure. The area of the piston in the master cylinder is 6.60 cm 2, and the area of the piston in the brake cylinder is 2.00 cm 2. The coefficient of friction between the brake shoe and the wheel drum is 0.5. Determine the frictional force between the brake shoe and the wheel drum when a force of 44 N is exerted on the pedal. 13

14 Capping one side of lift, PVnRT 14

15 Buoyant Force explained / derived 15

16 4.) A 1 m 3 cube of density 1400 kg/m 3 rests on the floor, with air surrounding it, ρair = 1.29 kg/m 3 a) What is the weight of the box b) What is the buoyant force acting on the box c) How much pressure does the box exert on the floor? 16

17 5.) Sea water has a density of 1025 kg/m 3. Ignoring frictional effects, how much force is needed to lift a 2000 kg sphere of radius 0.5 m in sea water 17

18 6.) A 14.7 kg gold crown is submerged in water and a scale reads 13.4 kg. Is the crown gold? 18

19 7.) A balloon has a total mass of 800 kg including the empty balloon. Given that the specific gravity of helium is , what is the volume of the spherical balloon needed to make the mass float? 19

20 STUDENTS DO 8.) A relaxed spring with a force constant of 16 N/m rests in a beaker filled with water. A 5 x 10 3 kg block of wood (650 kg/m 3 density) is pushed under the water, attached to the spring and released. How much does the spring stretch? 20

21 Composite objects 9.) A sphere has a radius of 1 m. The sphere is made of a metal with a center core of made of cork. The density of the metal is 1500 kg/m 3 and the density of the cork is 100 kg/m 3. This sphere is placed in the water, completely submerged, and remains motionless. What is the radius of the cork core? 21

22 STUDENTS DO 10.) A rectangular candle 10 cm wide x 10 cm thick x 20 cm high has a specific gravity of The candle is floating in water as shown in Figure A. (a) What is the density of the candle (b) What is the height of the candle above the water. (c) A newly designed ultra lightweight candle has a density half that of the candle from this problem. What percentage of the volume will be submerged in water d) If the candle was oriented as shown in figure B, how would that effect the height above water, how would the buoyant force be affected 22

23 STUDENTS DO 11.) A 1 kg hollow ball with a radius of 0.10 m is filled with air and released from rest at the bottom of a 2 m deep pool of water. How high above the water does the ball rise? (Disregard frictional effects and the motion of the ball while it is partially submerged) 23

24 ρair = 1.29 kg/m 3 12.) A cube with sides 2m long has a density of 2000 kg / m 3 and is sitting on the floor, in the surrounding air. a) How much buoyant force acts on the cube b) What is the amount of pressure that is exerted on the floor by the cube. (hint the cube has a certain amount of area in contact with the floor) c) The cube is placed in a pool 5 m deep and the cube comes to rest on the floor of the pool. What is the total pressure acting at the top of the cube. (Atmospheric pressure = 1.01x10 5 Pa) d) The center of the cube will be hollowed out and filled with air then placed in the pool again. What must the volume of this cavity be in order to make the cube sit at rest completely submerged just below the water surface (Hint: the air weight is very light in relation to the metal and compared to the buoyant force so it can be ignored) 24

25 Water Seeks its own Level Trick version 13.) Problem find height of second fluid 25

26 3. A glass U tube with a uniform diameter of cm is used to determine the density of an oil. As shown in the figure above, a 24.5 cm column of water balances a 27.2 cm column of the oil so that interfaces A and B of the mercury with the other liquids are at the same height. The density of water is 1.00 x 10 3 kg m 3. (a) Calculate the density of the oil. (b) Calculate the absolute pressure at B, the interface between the water and the mercury. A new tube, identical to the U tube except for a cone shape on the left, as shown above, is filled with the same volume of mercury that was in the U tube. The mercury is at the same height on both sides of the new tube as it was in the U tube, as shown by the dashed line. The same volumes of oil and water that were in the U tube are now poured into the new tube, on the left and right respectively. (c) Indicate the new position of B relative to A. Above A Below A At the same height as A Justify your answer. (d) A small piece of wood with density less than that of the oil is placed so that it floats in the left side of the tube. Indicate whether the pressure at the bottom of the tube increases, decreases, or remains the same. Increases Decreases Remains the same 26

27 14.) A box of unknown density is floating in a fluid with a density of 800 kg/m 3 with 60% of its volume submerged. a) Determine the density of the box. b) How much force would have to be applied to fully submerge the box c) If the box is placed in a fluid with density 900 kg/m 3, does it rise or sink? Determine the percentage of the box submerged 27

28 Fluid Statics Thought Puzzles 1.) A 100 cm 3 steel ball and a 100 cm 3 aluminum ball are both thrown into a water bath and sink to the bottom. Compare the buoyant force acting on each. 2.) A 1 kg lead block and a 1 kg copper block are dropped into a water bath, compare the buoyant force acting on each. 3.) A 50 cm 3 wood block and a 50 cm 3 steel block are placed into a water bath. Compare the buoyant force acting on each block 4.) A glass of water is filled all the way to the top at the brink of spilling and has ice cubes that are only partially submerged. As the ice melts, does the water remain the same level, decrease, or spill over the side. 5.) A cork is pushed underwater in a fish tank and held there. The cork is released and simultaneously the fish tank is dropped and falls. What happens to the cork. 6.) A pitcher of water is punctured at the base and water shoots out the bottom hole. The pitcher is then dropped and falls, how is the water stream affected. 7.) A boat is floating in a pool with a large rock in the boat. The rock is tossed over the side and sinks to the bottom of the pool. Does th level of water in the pool rise, sink or remain the same DEMO 28

29 29

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

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