Multiple Choice. AP B Fluids Practice Problems. Mar 22 4:15 PM. Mar 22 4:15 PM. Mar 22 4:02 PM

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1 P Fluids Practice Problems Mar 22 4:15 PM Multiple hoice Mar 22 4:15 PM 1 Two substances mercury with a density kg/m 3 and alcohol with a density 0.8 g/cm 3 are selected for an experiment. If the experiment requires equal masses of each liquid, what is the ratio of alcohol volume to the mercury volume? 1/15 1/17 1/13 1/10 17/1 1

2 2 perpendicular force is applied to a certain area and produces a pressure P. If the same force is applied to a twice bigger area, the new pressure on the surface is: 2P 4P P P/2 P/4 3 There are two round tables in the physics classroom: one with the radius of 50 cm the other with a radius of 150 cm. What is the relationship between the two forces applied on the tabletops by the atmospheric pressure? F 1 /F 2 = 1/3 F 1 /F 2 = 1/9 F 1 /F 2 = 3/1 F 1 /F 2 =9/1 F 1 /F 2 = 1/6 4 Three containers are used in a chemistry lab. ll containers have the same bottom area and the same height. chemistry student fills each of the containers with the same liquid to the maximum volume. Which of the following is true about the pressure on the bottom in each container? P1 > P2 > P3 P1 < P2 < P3 P1 < P2 > P3 P1 > P2 < P3 P1 = P2 = P3 2

3 5 What is the difference between the pressure on the bottom of a pool and the pressure on the water surface? ρgh ρg/h ρ/gh gh/ρ zero 6 boy swims a lake and initially dives 0.5 m beneath the surface. When he dives 1 m beneath the surface, how does the absolute pressure change? It doubles It quadruples It cut to a half It slightly increases It slightly decreases 7 Which of the following scientists invented a mercury barometer? laise Pascal vangelist Torricelli medeo vogadro Robert rown James Joule 3

4 8 car driver measures a tire pressure of 220 kpa. What is the absolute pressure in the tire? 321 kpa 119 kpa 0 kpa 101 kpa 220 kpa 9 In a hydraulic lift the small piston has an area of 2 cm 2 and large piston has an area of 80 cm 2. What is the mechanical advantage of the hydraulic lift? hydraulic lift is used to lift a car. The small piston has a radius of 5 cm and the large piston has a radius of 50 cm. If a driver applies a force of 88 N to the small piston, what is the weight of the car the large piston can support? 880 N 88 N 8800 N 8.8 N N 4

5 11 Three blocks of equal volume are completely submerged into water. The blocks made of different materials: aluminum, iron and lead. Which of the following is the correct statement about the buoyant force on each block? (ρaluminum = 2700 kg/m 3, ρ iron = 7800 kg/m 3, ρ lead = kg/m 3 ) F aluminum > F iron > F lead F aluminum < F iron < F lead F aluminum < F iron > F lead F aluminum = F iron = F lead F aluminum > F iron < F lead 12 piece of iron has a weight of 3.5 N when it is in air and 2.0 N when it is submerged into water. What is the buoyant force on the piece of iron? 3.5 N 2.0 N 1.5 N 1.0 N 0.5 N 13 Physics students use a spring scale to measure the weight of a piece of lead. The experiment was performed two times one in air the other in water. If the volume of lead is 50 cm 3, what is the difference between two readings on the scale? 0.5 N 5.0 N 50 N 500 N 0 N 5

6 14 solid cylinder of mass 5 kg is completely submerged into water. What is the tension force in the string supporting the cylinder if the specific gravity of the cylinder s material is 10? 5 N 0.5 N 50 N 45 N 10 N 15 n object has a weight of 9 N when it is in air and 7.2 N when it is submerged into water. What is the specific gravity of the object s material? wooden block with a weight of 7.5 N is placed on water. When the block floats on the surface of water it is partially submerged in water. What is the weight of the displaced water? 5.0 N 5.5 N 6.0 N 7.0 N 7.5 N 6

7 17 wooden block with a weight of 9 N is placed on water. When the block floats on the surface of water it is partially submerged in water. What is the volume of the displaced water? 500 cm cm cm cm cm 3 18 Water flows at a constant speed of 16 m/s through narrow section of the pipe. What is the speed of water in the section of the pipe where its radius is twice of the initial radius? 16 m/s 12 m/s 8 m/s 4 m/s 2 m/s 19 Venturi tubes have three sections with different radii. Which of the following is true about manometer readings? P 1 > P 2 > P 3 P 1 < P 2 < P 3 P 2 < P 1 < P 3 P 1 < P 2 > P 3 P 3 = P 2 = P 1 7

8 20 n open bottle is filled with a liquid which is flowing out trough a spigot located at the distance h below the surface of the liquid. What is the velocity of the liquid leaving the bottle? 2gh 4gh ρgh Free Response Mar 22 4:15 PM 1. small sphere of mass m and density is suspended from an elastic spring. The spring is stretched by a distance X 1. a. etermine the spring constant. The sphere is submerged into liquid of unknown density ρ <. The new displacement of the spring is X 2. b. On the diagram below show all the applied forces on the sphere when it is submerged. c. etermine the weight of the displaced liquid by the sphere. d. etermine the density of liquid. xpress your result in terms of, X 1, X 2. Mar 22 4:19 PM 8

9 1. small sphere of mass m and density is suspended from an elastic spring. The spring is stretched by a distance X 1. a. etermine the spring constant. Fs =W KX1=mg K =mg/x1 Mar 22 4:19 PM 1. small sphere of mass m and density is suspended from an elastic spring. The spring is stretched by a distance X 1. The sphere is submerged into liquid of unknown density ρ <. The new displacement of the spring is X 2. b. On the diagram below show all the applied forces on the sphere when it is submerged. Fouyant Fspring weight Mar 22 4:19 PM 1. small sphere of mass m and density is suspended from an elastic spring. The spring is stretched by a distance X 1. c. etermine the weight of the displaced liquid by the sphere. weight of water displaced is the same as the bouyant force. This force is equal to the weight of the sphere minus the force in the spring when the sphere is submerged weight of the sphere = kx1 force in the spring when the sphere is submerged is= kx2 W = Fb = kx1 kx2= k(x1 X2) = mg/x1 (X1 X2) = (mg) (1 X2/X1) Mar 22 4:19 PM 9

10 1. small sphere of mass m and density is suspended from an elastic spring. The spring is stretched by a distance X 1. d. etermine the density of liquid. xpress your result in terms of, X 1, X 2. ρvg = Fb V= m/ so ρmg/ = mg (1 X2/X1) ρ = (1-X2/X1) Mar 22 4:19 PM 2. pool has an area = 50 m 2 and depth h = 2.5 m. The pool is filled with water to the maximum height. n electrical pump is used to empty the pool. There are two pipes coming out the pump: one is submerged into water has a radius r 1 = 4 cm the other has a radius r 2 = 2.5 cm. nswer the following questions ignoring friction, viscosity, turbulence. a. alculate the net force on the bottom of the pool. b. alculate work done by the pump required to empty the pool in 5 h. c. alculate the speed of the water flow in the submerged pipe. The pump produces a pressure P1 = 9*10 5 Pa in the submerged pipe. d. alculate speed of the water flow in the second section of the pipe placed on the ground. Mar 22 4:25 PM 2. pool has an area = 50 m 2 and depth h = 2.5 m. The pool is filled with water to the maximum height. n electrical pump is used to empty the pool. There are two pipes coming out the pump: one is submerged into water has a radius r 1 = 4 cm the other has a radius r 2 = 2.5 cm. nswer the following questions ignoring friction, viscosity, turbulence. a. alculate the net force on the bottom of the pool. F = Pabs = (ρgh + Patn) = mg + Patm* = Vg= 1000 x125 * *50= 6.3x10 6 N Mar 22 4:25 PM 10

11 2. pool has an area = 50 m 2 and depth h = 2.5 m. The pool is filled with water to the maximum height. n electrical pump is used to empty the pool. There are two pipes coming out the pump: one is submerged into water has a radius r 1 = 4 cm the other has a radius r 2 = 2.5 cm. nswer the following questions ignoring friction, viscosity, turbulence. b. alculate work done by the pump required to empty the pool in 5 h. W=Fd = mgh =125*1000*9.8*1.25 = 1.5 x10 6 J Mar 22 4:25 PM 2. pool has an area = 50 m 2 and depth h = 2.5 m. The pool is filled with water to the maximum height. n electrical pump is used to empty the pool. There are two pipes coming out the pump: one is submerged into water has a radius r 1 = 4 cm the other has a radius r 2 = 2.5 cm. nswer the following questions ignoring friction, viscosity, turbulence. c. alculate the speed of the water flow in the submerged pipe. The mass flow rate is mass/time = ρ v v = mass/(time area density) = (density volume)/(time area density) = volume/(time area) = 125m 3 / (18000s 3.14 (0.04) 2 ) =1.38m/s Mar 22 4:25 PM 2. pool has an area = 50 m 2 and depth h = 2.5 m. The pool is filled with water to the maximum height. n electrical pump is used to empty the pool. There are two pipes coming out the pump: one is submerged into water has a radius r1 = 4 cm the other has a radius r2 = 2.5 cm. nswer the following questions ignoring friction, viscosity, turbulence. The pump produces a pressure P1 = 9*10 5 Pa in the submerged pipe. d. alculate speed of the water flow in the second section of the pipe placed on the ground. constant / = / v v 2 = v= (776452/500)= 39.4m/s Mar 22 4:25 PM 11

12 3. submarine dives from rest a 100 m distance beneath the surface of an ocean. Initially the submarine moves at a constant rate 0.3 m/s 2 until reaches a speed of 4 m/s and then lowers at a constant speed. The density of salt water is 1030 kg/m 3. The submarine has a hatch with an area of 2 m 2 located on the top of the submarine s body. a. How much time it takes for the submarine to move down 100 m? b. alculate the gauge pressure applied on the submarine at the depth of 100 m. c. alculate the absolute pressure applied on the submarine at the depth of 100m. d. How much force is required in order to open the hatch from the inside of submarine? Mar 22 4:30 PM 3. submarine dives from rest a 100 m distance beneath the surface of an ocean. Initially the submarine moves at a constant rate 0.3 m/s 2 until reaches a speed of 4 m/s and then lowers at a constant speed. The density of salt water is 1030 kg/m 3. The submarine has a hatch with an area of 2 m 2 located on the top of the submarine s body. a. How much time does it take for the submarine to move down 100 m? v 2 =vo 2 +2ax 4 2 =0+2ax x=16/.6 = 26.67m t1=(2x/.3) 1/2 =13.33s t2= ( ) /4 =18.3s t= =31.7s Mar 22 4:30 PM 3. submarine dives from rest a 100 m distance beneath the surface of an ocean. Initially the submarine moves at a constant rate 0.3 m/s 2 until reaches a speed of 4 m/s and then lowers at a constant speed. The density of salt water is 1030 kg/m 3. The submarine has a hatch with an area of 2 m 2 located on the top of the submarine s body. b. alculate the gauge pressure applied on the submarine at the depth of 100 m. Pgauge = ρgh = = Pa = 1.01 x10 6 Pa Mar 22 4:30 PM 12

13 3. submarine dives from rest a 100 m distance beneath the surface of an ocean. Initially the submarine moves at a constant rate 0.3 m/s 2 until reaches a speed of 4 m/s and then lowers at a constant speed. The density of salt water is 1030 kg/m 3. The submarine has a hatch with an area of 2 m 2 located on the top of the submarine s body. c. alculate the absolute pressure applied on the submarine at the depth of 100m. Pabs = Pgauge + Patm = 1.01 MPa kpa = 1.11 MPa Mar 22 4:30 PM 3. submarine dives from rest a 100 m distance beneath the surface of an ocean. Initially the submarine moves at a constant rate 0.3 m/s 2 until reaches a speed of 4 m/s and then lowers at a constant speed. The density of salt water is 1030 kg/m 3. The submarine has a hatch with an area of 2 m 2 located on the top of the submarine s body. d. How much force is required in order to open the hatch from the inside of submarine? F = Pgauge = 1.01Mpa *2 m 2 = 2.02 MN Gauge pressure is used and not abolute because the assumption is made that inside the submarine the air pressure is the same as the atmospheric pressure at sea level. The internal pressure balances the additional atmospheric pressure. However, the question remains why would you open the hatch when you are 100 m under water? Mar 22 4:30 PM 4. rectangular slab of ice floats on water with a large portion submerged beneath the water surface. The volume of the slab is 20 m 3 and the surface area of the top is 14 m 2. The density of ice is 900 kg/m 3 and sea water is 1030 kg/m 3. a. On the diagram below show all the applied forces on the slab. b. alculate the buoyant force on the slab. c. alculate the height h of the portion of the slab that is above the water surface. polar bear climbs to the top of the slab and sits on the slab for a long time. d. On the diagram below show all the applied forces on the slab. Mar 22 4:32 PM 13

14 4. rectangular slab of ice floats on water with a large portion submerged beneath the water surface. The volume of the slab is 20 m 3 and the surface area of the top is 14 m 2. The density of ice is 900 kg/m 3 and sea water is 1030 kg/m 3. a. On the diagram below show all the applied forces on the slab. F Fg Mar 22 4:32 PM 4. rectangular slab of ice floats on water with a large portion submerged beneath the water surface. The volume of the slab is 20 m 3 and the surface area of the top is 14 m 2. The density of ice is 900 kg/m 3 and sea water is 1030 kg/m 3. b. alculate the buoyant force on the slab. The buoyant force is the same as the weight of the ice F = mg =ρvg = = 1.8x10 5 N Mar 22 4:32 PM 4. rectangular slab of ice floats on water with a large portion submerged beneath the water surface. The volume of the slab is 20 m 3 and the surface area of the top is 14 m 2. The density of ice is 900 kg/m 3 and sea water is 1030 kg/m 3. c. alculate the height h of the portion of the slab that is above the water surface. Vdisp/Vo = ρo/ρf since this is a rectangular slab with the same base area everywhere Vdisp = area x hsub hsub= 900/1030*20/14 = habove water = hice - hsub = 20/ = = 0.180m Mar 22 4:32 PM 14

15 4. rectangular slab of ice floats on water with a large portion submerged beneath the water surface. The volume of the slab is 20 m 3 and the surface area of the top is 14 m 2. The density of ice is 900 kg/m 3 and sea water is 1030 kg/m 3. polar bear climbs to the top of the slab and sits on the slab for a long time. d. On the diagram below show all the applied forces on the slab. F buoyant Wbear Wice Mar 22 4:32 PM Feb 11 10:09 PM 15

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