PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HOMEWORK PROBLEMS Chapter 9 SOLIDS AND FLUIDS HW 9 PART A Hand in your answers in class on scantron on Monday November 2010 Write your name class 1401 and HW 9 on the scantron 1 What is the mass of a solid gold rectangular bar that has dimensions of 4 50 cm x 11 0 cm x 26 0 cm a 24 8 kg b 45 6 kg c 11 4 kg d 33 2 kg e 19 5 kg m r gold V 19 3 103 kg m3 4 50 10 2 m 11 0 10 2 m 26 0 10 2 m 24 8 kg 2 A 66 0 kg man lies on his back on a bed of nails with 1 208 of the nails in contact with his body The end of each nail has area 1 00 x 10 6 m2 What average pressure is exerted by one nail on the man s body a 2 21 x 105 Pa b 3 09 x 105 Pa c 1 65 x 106 Pa d 5 35 x 105 Pa 4 e 4 11 x 10 Pa On average the support force each nail exerts on the body is 66 0 kg 9 80 m s2 mg 0 535 N 1 208 1 208 so the average pressure exerted on the body by each nail is F 0 535 N Pav 1 5 35 105 Pa Anail 1 00 10 6 m 2 F1 end 3 A hydraulic jack has an input piston of area 0 050 m2 and an output piston of area 0 70 m2 How much force on the input piston is required to lift a car weighing 1 2 x 103 N a 42 N b 68 N c 86 N d 110 N e 130 N From Pascal s principle F1 A1 F2 A2 so if the output force is to be F2 1 2 103 N the required input force is A 0 050 m 2 F1 1 F2 1 2 103 N 86 N 0 70 m 2 A2 4 A lead bullet is placed in a pool of mercury What fractional part of the volume of the bullet is submerged a 0 455 b 0 622 c 0 714 d 0 831 e 0 930 According to Archimedes s principle the buoyant force exerted on the bullet by the mercury is equal to the weight of a volume of mercury that is the same as the submerged volume of the bullet If the bullet is to float this buoyant force must equal the total weight of the bullet Thus for a floating bullet r mercury Vsubmerged g r lead Vbullet g and Vsubmerged Vbullet r lead r mercury 11 3 103 kg m 3 0 831 13 6 103 kg m 3 1 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 9 5 What is the pressure at the bottom of Loch Ness which is as much as 754 ft deep The surface of the lake is only 15 8 m above sea level hence the pressure there can be taken to be 1 013 x 105 Pa a 1 52 X 105 Pa b 2 74 X 105 Pa c 2 35 X 106 Pa d 7 01 X 105 Pa 5 e 3 15 X 10 Pa The absolute pressure at depth h below the surface of a liquid with density r and with pressure P0 at its surface is P P0 r gh Thus at a depth of 754 ft in the waters of Loch Ness P 1 013 10 5 Pa 1 00 10 3 kg m 3 9 80 1 m 6 m s2 754 ft 2 35 10 Pa 3 281 ft 6 Hurricane winds of 95 mi h are blowing over the flat roof of a well sealed house What is the difference in air pressure between the inside and outside of the house a 1 2 X 103 Pa b 2 4 X 104 Pa c 3 4 X 103 Pa d 4 0 X 103 Pa 4 e 5 3 X 10 Pa We assume that the air inside the well sealed house has essentially zero speed and the thickness of the roof is negligible so the air just above the roof and that just below the roof is at the same altitude Then Bernoulli s equation gives the difference in pressure just below and just above the roof with the pressure below being the greatest as 1 P1 P2 r air v22 v12 r air g y2 y1 2 or 2 1 1 3 DP 1 29 kg m 95 mi h 0 0 1 2 10 3 Pa 2 2 237 mi h 7 A horizontal pipe narrows from a radius of 0 250 m to 0 100 m If the speed of the water in the pipe is 1 00 m s in the larger radius pipe what is the speed in the smaller pipe a 4 50 m s b 2 50 m s c 3 75 m s d 6 25 m s e 5 13 m s From the equation of continuity A1v1 A2 v2 the speed of the water in the smaller pipe is p 0 250 m 2 A1 v2 v1 p 0 100 m 2 A2 1 00 m s 6 25 m s 8 Bernoulli s equation can be used to explain in part which of the following phenomena a the lift on an airplane wing in flight b the curve of a spinning baseball c vascular flutter d reduction in pressure of moving fluids e all these answers All of these phenomena are the result of a difference in pressure on opposite sides of an object due to a fluid moving at different speeds on the two sides Thus the correct response to this question is choice e Bernoulli s equation can be used in the discussion of each of these phenomena 2 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 9 9 A boat develops a leak and after its passengers are rescued eventually sinks to the bottom of a lake When the boat is at the bottom is the normal force on the boat a greater than the weight of the boat b equal to the weight of the boat c less than the weight of the boat d equal to the weight of the displaced water or e equal to the buoyant force on the boat The boat even after it sinks experiences a buoyant force B equal to the weight of whatever water it is displacing This force will support part of the weight w of the boat The normal force exerted on the boat by the bottom of the lake will be n w B w will support the balance of the boat s weight The correct response is c 10 Three vessels of different shapes are filled to the same level with water as in Figure MCQ9 10 The area of the base is the same for all three vessels …