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Physics Unit 5 This Slideshow was developed to accompany the textbook OpenStax Physics Available for free at https://openstaxcollege.org/textbooks/collegephysics By OpenStax College and Rice University 2013 edition Some examples and diagrams are taken from the textbook. Slides created by Richard Wright, Andrews Academy rwright@andrews.edu Phases of Matter Solid Atoms in close contact so they can’t move much Set volume and shape Can’t compress Liquid Atoms move past each other Set volume Takes shape of container Hard to compress Gas Atoms far apart Neither set volume or shape Compressible Fluids Flow Both liquids and gases Density = Where = density m = mass V = Volume Things with small density float on things with more density Solids most dense Gases least dense See Table 11.1 Can use density to determine unknown material An ornate silver crown is thought to be fake. How could we determine if is silver without damaging the crown? Find its mass using a balance. (It is 1.25 kg) Find its volume by submerging in water and finding volume of displaces water. (It is 1.60 × 10−4 m3) Find the density = 7.81 × 103 kg/m3 Table 11.1 says it is steel Silver’s density is 10.5 × 103 kg/m3 Don’t be dense, you can solve these problems 11P1-7 Read 11.3, 11.4 11CQ8, 9, 11, 13, 14, 16, 17 Answers: 1) 1.610 cm3 2) 2.54 L 3) 2.58 g 4) 2.70 g/cm3 5) 3.99 cm 6) 0.163 m 7) 2.86 times denser The molecules in a fluid are free to wander around In their wanderings they sometimes collide with the sides of their container (i.e. balloon) The more the molecules collide with the walls, the more force is felt = P = Pressure F = Force perpendicular to surface A = Area of surface Unit: N/m2 = Pa (pascal) 1 Pa is very small so we usually use kPa or atm In a fluid the pressure is exerted perpendicularly to all surfaces A static fluid cannot produce a force parallel to a surface since it is not moving parallel to surface You are drinking a juice box. In the process you suck all the juice and air out of the box. The top of the box is 7.5 cm by 5 cm. If the air pressure is 1.013 × 105 Pa, how much force is acting on the top of the box? 380 N = 85 lbs Would the force of the side of the box be more or less than the top? More because more area The force that squashes the juice box is from the weight of all the air above it Atmospheric Pressure at Sea Level 1.013 × 105 Pa = 1 atmosphere (1 atm) The column of static fluid experiences several vertical forces Since the fluid is not moving, it is in equilibrium and ∑ = 0 ∑ = 2 − 1 − = 0 2 = 1 + = 2 = 1 + = ℎ 2 = 1 + ℎ 2 = 1 + ℎ Or = ℎ where P is the pressure due to the fluid at a depth h below the surface → = If the pressure is known at a depth, the pressure lower down can be found by adding ρgh This assumes ρ is constant with depth This is a good estimate for liquids, but not for gasses unless h is small Would Hoover Dam need to be just as strong if the entire lake behind the dam was reduced to an inch of water behind the dam, but the same depth as the lake? Yes, the pressure depends only on the depth What is the total pressure at points A and B? 1.55x105 Pa Yes, there is a lot of pressure riding on this assignment 11P11-17, 20, 22 Read 11.5, 11.6 11CQ24-27 Answers: 11) 3.59 × 106 Pa 12) 7.80 × 104 Pa 13) 2.36 × 103 N 14) 0.760 m 15) 1.10 × 108 Pa 16) Show work 17) 30.6 m 20) 1.09 × 103 Pa 22) 24.0 N Pascal’s Principle A change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and the walls of its container. Basis of hydraulics Since = , if we change the area, the force is changed How much force must be exerted at A to support the 850-kg car at B? The piston at A has a diameter of 17 mm and the piston at B a diameter of 300 mm. F = 26.7 N A B Gauge Pressure Used by pressure gauges Measures pressure relative to atmospheric pressure Absolute Pressure Sum of gauge pressure and atmospheric pressure = + Open-Tube Manometer U-shaped tube with fluid in it One end is connected to the container of which we want to measure the pressure The other end is open to the air 2 = 2 = ℎ + 2 − = Barometer Used to measure air pressure A tube with the top sealed and filled with mercury The bottom is open and sitting in a pool of mercury Pressure at top = 0 Pressure at bottom = = ℎ Let me pressure you into solving these problems 11P24-27, 30-34 Read 11.7 11CQ28-31 Answers: 24) 2.55 × 107 Pa, 251 atm 25) 136 N 26) 5.76 × 103 N 27) 100:1, 10:1, 1:100 30) 1.60 × 104 Pa, 1.07 × 104 Pa 31) 4.08 m 32) 1.49 × 106 N 33) 159 / 119 34) 3.99 × 104 N Think of trying to push a beach ball under water The water pushes it up All fluids push things up because the pressure is higher at greater depths The upward force is buoyant force = 2 − 1 = 2 − 1 2 = 1 + ℎ 2 − 1 = ℎ = ℎ = = ℎ = ℎ = = = Archimedes’ Principle Buoyant force = weight of the displaced fluid = If buoyant force ≥ gravity, then it floats If buoyant force < gravity, then it sinks An ice cube is floating in a glass of fresh water. The cube is 3 cm on each side. If the cube is floating so a flat face is facing up, what is the distance between the top of the cube and the water? h 0.002 m x As you might have guessed An object will float if its average density < density of the fluid In other words, it will float if it displaces more fluid than its own weight Specific Gravity = = fraction submerged If specific gravity < 1 it floats If specific gravity > 1 it sinks A man tied a bunch of helium balloons to a lawn chair and flew to a great altitude. If a single balloon is estimated as a sphere with a radius of 20 cm and is filled with helium, what is the net force on one balloon? 0.3648 N How many balloons would be required to lift a 80 kg man and chair? 2150 balloons Be buoyed up the thought of the joy derived from solving these problems 11P 37-42, 44, 51 Read 11.8, 11.9 11CQ33-38 Answers: 37) 800 kg/m3 38) 815 kg/m3 39) 99.5%, 96.9% 40) 41.4 g, 41.4 cm3, 1.09 g/cm3 41) 198 g, 198 cm3, 2.73 g/cm3 42) 39.5 g, 50 cm3, 0.79 g/cm3, ethyl alcohol 44) 8.21 N 51) 2920 N Cohesive Forces Forces between molecules of same type Holding water together in cup Adhesive Forces Forces between molecules of different type Water drops sticking to grass Surface Tension Cohesive forces at surface of a liquid cause it to have smallest surface area possible Why drops are round Sort of like membrane on top of fluid Proportional to cohesive force which varies by fluid = = surface tension F = force L = length on the surface the force is applied Gauge pressure inside spherical bubble Inward surface tension causes pressure inside a bubble to be higher than atmospheric pressure = 4 Interaction of cohesion and adhesion A drop of water on a surface Cohesion wants to make a spherical drop Adhesion wants to spread out and stick to surface Contact angle Indicates which force is stronger Capillary Action Tendency of a fluid to be drawn up a narrow, capillary, tube If contact angle is < 90°, then fluid raised up tube As the fluid touches the sides of tube, adhesive forces pull fluid up, cohesive forces pull the center up, but not as much The curved part is called meniscus Height that capillary action can lift fluid ℎ = 2 cos = surface tension = density of fluid = acceleration of gravity = radius of tube Calculate the gauge pressure inside two soap bubbles with radii of 3 cm and 1 cm. 3 cm: 4.93 Pa 1 cm: 14.8 Pa That’s why it’s harder to blow up a small balloon than a big balloon. Stick with it, you can do well 11P54-59, 62-63, 68-69, 73-74, 77 Read 12.1, 12.2 12CQ1-5, 9-12, 14 Answers: 54) 592 N/m2 55) 0.0700 N/m, water at 40°C 56) 2.23 × 10−2 mmHg 57) 1.56 × 10−3 N 58) 1.65 × 10−3 m, 3.71 × 10−4 m 59) 0.566 m 62) 14.6 N/m2, 4.46 N/m2, 7.40 N/m2, Alcohol 63) -1.46 cm, 0 cm 68) 479 N 69) 5.00 × 108 Pa 73) 3.81 × 103 N/m2, 28.7 mmHg 74) 27.1 cm 77) 3.98 × 106 Pa, 2.1 × 10−3 cm Flow Rate = Q = Flow rate V = Volume of fluid t = time = = = A = cross-section area = average velocity of fluid Since flow rate is constant for a given moving fluid Equation of continuity 1 1 1 = 2 2 2 If incompressible 1 1 = 2 2 If incompressible and several branches 1 1 1 = 2 2 2 Where does the water flow the fastest? A B C A garden hose has a diameter of 2 cm and water enters it at 0.5 m/s. You block 90% of the end of the hose with your thumb. How fast does the water exit the hose? v = 5 m/s When a fluid goes through narrower channel, it speeds up It increases kinetic energy = 1 2 2 − 1 02 2 Net work comes from pressure pushing the fluid Derivation = − 0 = + 1 = 2 + ℎ 2 = ⋅ = → = → = = 2 − 1 = 2 − 1 = 1 12 2 Divide by V and rearrange = + ℎ1 − 1 22 2 + ℎ2 Bernoulli’s Equation 1 2 1 2 1 + 1 + ℎ1 = 2 + 2 + ℎ2 2 2 Think about driving down a road with something in your car trunk. The object is too large to completely shut the trunk lid. While the car is stopped, the lid quietly rests as far down as it can go. As you drive down the road, why does the trunk open? The air in the trunk is still. The air above the trunk is moving. The air in the trunk is at a higher pressure than above the trunk. So the trunk is pushed open. Demo: Fold paper into a tunnel and blow through it. What happens and why? Why is an aneurysm (enlarged region of a blood vessel) bad for you? As the blood enters the enlarged region, it slows. The slower blood has a higher pressure, and pop! Why do all houses need a plumbing vent? Waste water flows through a sewer line. Something like a sink is connected to the line, but there is a water trap to keep the sewer gasses from entering the house. The flowing water in the sewer means the air directly above the flowing water has a lower pressure than the air above the sink. This pushes the water in the trap down the pipe and sewer gasses enter the house How do airplane wings work (even paper airplanes)? The top of the wing is curved and the bottom is not. The air flows faster over the top of the wing, than the bottom. This pushes the wing up. How does a curve ball in baseball work? The faster you work, the less pressure you’ll feel? 12P2-6, 8, 11, 20-23 Read 12.3 12CQ18-21 Answers: 2) 83.3 cm3/s, 8.33 × 10−5 m3/s 3) 27 cm/s 4) 5.03 cm3/s, 151 cm3 5) 0.75 m/s, 0.13 m/s 6) 0.1391 8) 0.166 cm/s 11) 12.6 m/s, 0.0800 m3/s 20) 33.1 m, 19.6 cm 21) 2.54 × 105 N 22) 15.3 N 23) 1.58 × 106 N/m2, 163 m Previous examples of Bernoulli’s Equation had simplified conditions Bernoulli’s Equation work in real world Water circulates throughout a house in a hot-water heating system. If the water is pumped at a speed of 0.50 m/s through a 4.0-cm-diameter pipe in the basement under a pressure of 3.0 atm, what will be the flow speed and pressure in a 2.6-cm-diameter pipe on the second floor 5.0 m above? Assume the pipes do not divide into branches. 2 = 1.2 2 = 2.5 The tank is open to the atmosphere at the top. Find an expression for the speed of the liquid leaving the pipe at the bottom. 1 = 2ℎ Since Bernoulli’s Equation is conservation of energy, the water would rise up to the same height as the water in the tank. Power in Fluid Flow Power is rate of work or energy Bernoulli’s Equation terms are in energy per volume Multiply Bernoulli’s Equation by volume and divide by time Or multiply by flow rate Q = + 1 2 2 Apply yourself to these applications 12P25-28 Read 12.4, 12.5 12CQ22-24, 26-28 Answers: 25) 9.56 × 108 W, 2.12 26) 71.8 m/s, 257 m/s 27) 1.26 W 28) 2.76 × 105 , 2.81 × 105 Viscosity Fluid friction Turbulent Laminar Flow Smooth flow in layers that don’t mix Turbulent Flow Has eddies and swirls that mix layers of fluid Laminar How viscosity is measured Two plates with fluid between Top plate moved Friction causes the fluid to move = Laminar flow in tubes Difference in pressure causes fluids to flow 2 − 1 = Where Q is flow rate 1 and 2 are pressures R is resistance Poiseuille’s law for resistance 8 = 4 Where is viscosity l is length of tube r is radius of tube Since flow rate depends on pressure If Q is high, the pressure must decrease like Bernoulli’s equation If R is high, the pressure must decrease. In blood vessels this is a problem with plaque on artery walls How to tell if laminar or turbulent flow Low speed with smooth, streamlined object laminar High speed or rough object turbulent Reynolds number Below 2000 laminar Above 3000 turbulent Between 2000 and 3000 depends on conditions 2 = A hypodermic syringe is filled with a solution whose viscosity is 1.5 × 10−3 Pa ⋅ s. The plunger area of the syringe is 8.0 × 10−5 m2 , and the length of the needle is 0.025 m. The internal radius of the needle is 4.0 × 10−4 m. The gauge pressure in a vein is 1900 Pa (14 mmHg). What force must be applied to the plunger, so that 1.0 × 10−6 m3 of solution can be injected in 3.0 s? = 0.25 N Is the flow laminar if the density is 1000 kg/m3? = 4.44; Yes Let the answers flow 12P30-33, 35-37, 51-54, 56 Read 12.6, 12.7 12CQ29-33 Answers: 30) 1.61 × 10−5 31) 1.60 cm3/min 32) 0.0314 N, 0.471 mW 33) 8.7 × 10−2 3 / 35) 0.3161 36) 1.81 37) 1.52, higher blood pressure 51) 1990 52) show work 53) 127000, 35100 54) 790000, 1690000 56) 3.16 × 10−4 3 / If object move in fluid (or fluid moves past object) Alternate form of Reynolds number ′ = ′ < 1 laminar flow 1 < ′ < 10 transition, might have turbulent wake 10 < ′ < 106 either ′ > 106 turbulent Viscous drag Force trying to stop object in fluid If ′ < 1, ∝ v If 10 < ′ < 106 , ∝ 2 Terminal velocity Objects falling in fluid Viscous drag will increase as speed increases Eventually drag force will = gravity force No acceleration Diffusion Molecules in fluids move randomly They will travel some distance and then hit another molecule Average distance traveled = 2 How long will it take hemoglobin to move 1 mm in water by free diffusion ( = 6.9 × 10−11 2 /)? t = 7246 s = 2 h Diffusion Goes from high concentration to low Faster with higher difference of concentrations Diffusion across Membranes Membranes are barriers They are semipermeable Some molecules can cross, but others can’t Osmosis Transport of water through membrane from differences in concentration Dialysis Transport of other molecules through membrane from differences in concentration Reverse osmosis/reverse dialysis Sufficient pressure is applied to reverse normal direction of substance through membrane Can be used to purify a fluid Water pushed through a membrane that won’t let salt through You cannot learn by osmosis since knowledge is not water, you must study 12P38-39, 62-64, 66 Answers: 38) = 2 2 2 −1 9 39) 225 mPa⋅s 62) 1.41 mm 63) 130 64) 130 s 66) 0.391 s