About Midterm Exam 3 l When and where çThurs April 21 th, 5:45-7:00 pm çRooms: Same as Exam I and II, See course webpage. çYour TA will give a brief review during the discussion session. l Coverage: Chapts 9 – 12 (4 chapters) l Format çClosed book, 20 multiple-choices questions (format as in practice exams) ç1 page 8x11 formula sheet allowed, must be self prepared, no photo copying/download-printing of solutions, lecture slides, etc. çBring a calculator (but no lap-top computer). Only basic calculation functionality can be used. Bring a 2B pencil for Scantron. çFill in your ID and section # ! l Special requests: çIf different from Exam II, me at çOne alternative exam: 3:30pm – 4:45pm, Thurs Mar. 24, Cham 5280 (as before). 14/18/11Phys 201, Spring 2011

4/18/11Phys 201, Spring Chapter 13: Fluids Lecture 25 çDensity çPressure in fluids çVariation of pressure with depth in a fluid çBuoyancy and Archimedes’ principle

4/18/11Phys 201, Spring Liquid l Has a definite volume l No definite shape l Exist at a higher temperature than solids l The molecules “wander” through the liquid in a random fashion çThe intermolecular forces are not strong enough to keep the molecules in a fixed position

4/18/11Phys 201, Spring Gas l Has no definite volume l Has no definite shape l Molecules are in constant random motion l The molecules exert only weak forces on each other l Average distance between molecules is large compared to the size of the molecules

4/18/11Phys 201, Spring l Density = Mass/Volume çρ = M / V çunits = kg/m 3 Density

4/18/11Phys 201, Spring Pressure = Force per Unit Area Which will hurt more? çIf you are pricked by a nail with a force equal to your weight çIf your entire weight is supported by a bed of similar nails çBoth will hurt the same

4/18/11Phys 201, Spring Pressure in a fluid or gas Impulse to book: (or raindrops on your umbrella) Force is perpendicular to surface Force proportional to area of surface pressure (p) p = Force/area [N/m 2 ] 1 N/m 2 = 1 Pascal (Pa) v v FxFx book Air molecule

4/18/11Phys 201, Spring Atmospheric Pressure Even when there is no breeze, air molecules are continuously bombarding everything around - results in pressure. Normal atmospheric pressure = 1.01 x 10 5 Pa

4/18/11Phys 201, Spring Pressure and Depth l Examine the darker region, assumed to be a fluid ρ çIt has a cross-sectional area A çExtends to a depth h below the surface l Three external forces act on the region l -P 1 A + P 2 A - Mg = 0 l P 2 = P 1 + Mg/A = P 1 + Mgh/V = P 1 + ρgh l At the surface compared to at depth h l P o is normal atmospheric pressure ç1.013 x 10 5 Pa = 14.7 lb/in 2 P is the “absolute pressure”; P - P o is the “gauge pressure”

4/18/11Phys 201, Spring Barometer: Measure atmospheric pressure h p 2 =p atm p 1 =0 p 2 = p 1 + ρ gh p atm = ρ gh Measure h, determine p atm example--Mercury ρ = 13,600 kg/m 3 p atm = 1.05 x 10 5 Pa ρ h = m = 757 mm (for 1 atm)

4/18/11Phys 201, Spring Question: Is it possible to stand on the roof of a five story (50 foot) tall house and drink, using a straw, from a glass on the ground? 1. No 2. Yes The pressure that the air pushes down on the liquid in the glass is not enough to push all of the liquid up the 50ft through the straw. CORRECT PaPa h P=0 Evacuate the straw by sucking How high will water rise? no more than h = P a / ρ g (= 1.05 x 10 5 /1000/9.8) = 33 ft 8” no matter how hard you suck!

4/18/11Phys 201, Spring Measurement of Pressure l Manometer çIf both sides of an U-tube are open to atmosphere the levels of the fluid are the same on both sides çIf one side is connected to a “pressurized side” the level difference between the two sides can be used to measure pressure.

4/18/11Phys 201, Spring Measuring Blood Pressure l Blood pressure is quite high, 120/80 mm of Hg l Use higher density fluid in a manometer: Mercury

4/18/11Phys 201, Spring Forces on a Dam

4/18/11Phys 201, Spring Pascal’s Principle l The pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container. l This principle is used in hydraulic system çP 1 = P 2  (F 1 / A 1 ) = (F 2 / A 2 ) çCan be used to derive large gain by making A 2 much larger than A 1 »F 2 = F 1 (A 2 / A 1 ) »Work done is the same: height by which the surface A 2 rises is smaller than the change in the height of surface with area A 1. A1A1 F1F1 F2F2 A1A1 A2A2

Buoyancy and Archimedes’ Principle 4/18/11Phys 201, Spring B = ρ f V g

King Hiero II of Syracuse’s Crown l King Hiero II asked Archimedes to check if his crown was pure gold. l Archimedes knew ρ gold = 19.3x10 3 kg/m 3, ρ w = 1.00x10 3 kg/m 3 weighed: W c = F g = 7.84 N in air W’ c = F’ g = 6.86 N in water 4/18/11Phys 201, Spring l Archimedes’ principle: B = W c - W’ c = 0.98 N = F w = V ρ w g  V g = 0.98 N/ ρ w l Thus, the crown density: ρ c = M/V = W c / V g = (7.84 N /0.98 N) ρ w = 8 kg/m 3 < ρ gold King Hiero II was cheated !