PHYS 1443 – Section 501 Lecture #9AnnouncementsForces of FrictionExample w/ FrictionNewton’s Second Law & Uniform Circular MotionExample of Uniform Circular MotionExample of Banked HighwayWednesday, Feb. 18, 2004 PHYS 1443-501, Spring 2004Dr. Andrew Brandt1PHYS 1443 – Section 501Lecture #9•Forces of Friction•Uniform and Non-uniform Circular MotionsWednesday, February 18, 2004Dr. Andrew BrandtWednesday, Feb. 18, 2004 2 PHYS 1443-501, Spring 2004Dr. Andrew BrandtAnnouncements•HW #3 on Ch. 4 due tonight at midnight•Beware negative points•HW#4 on Ch. 5 due Mon Feb. 23•If you are struggling, read text before+after class, start HW early, ask questions, physics clinic--RM 10•Remember the 1st midterm, Weds., Feb. 25,–Covers chapters 1-5•Short Review on Monday, start ch. 6 unless questionsWednesday, Feb. 18, 2004 3 PHYS 1443-501, Spring 2004Dr. Andrew BrandtForces of FrictionnfssResistive force exerted on a moving object due to viscosity or other types of frictional properties of the medium in or surface on which the object moves.Force of static friction, fs:Force of kinetic friction, fkThe resistive force exerted on the object until just before the beginning of its movementThe resistive force exerted on the object during its movementnfkkThese forces are either proportional to velocity or normal forceEmpirical Formula What does this formula tell you? Frictional force is variable—as you push/pull harder it increases until it reaches the static limit!!Beyond the limit, there is no more static frictional force but kinetic frictional force takes it over.exampleWednesday, Feb. 18, 2004 4 PHYS 1443-501, Spring 2004Dr. Andrew BrandtExample w/ FrictionSuppose a block is placed on a rough surface inclined relative to the horizontal. The inclination angle is increased till the block starts to move. Show that by measuring this critical angle, c, one can determine coefficient of static friction, s.FFree-bodyDiagramxyMaFgnnF= -Mgfs=knyFxFsNet forcex comp.y comp.sfnxyaMsgfnF sgxfFsfMgsin0nscMgsinyMagyFncMgncos0gyFcMgcosnMgcsinccMgMgcossinctanwhat if 0cq =quiz&exampleWednesday, Feb. 18, 2004 5 PHYS 1443-501, Spring 2004Dr. Andrew BrandtNewton’s Second Law & Uniform Circular MotionFrFrrmrvar2The centripetal acceleration is always perpendicular to the velocity vector, v, for uniform circular motion.The force that causes centripetal acceleration acts toward the center of the circle and causes a change in the direction of the velocity vector. This force is called centripetal force.Are there forces in this motion? If so, what do they do?rFWhat do you think will happen to the ball if the string that holds the ball breaks? Why?Based on Newton’s 1st law, since the external force no longer exist, the ball will continue its motion without change and will fly away following a tangential direction to the circle.rmarvm2Wednesday, Feb. 18, 2004 6 PHYS 1443-501, Spring 2004Dr. Andrew BrandtExample of Uniform Circular MotionA ball of mass 0.500kg is attached to the end of a 1.50m long cord. The ball is moving in a horizontal circle. If the string can withstand maximum tension of 50.0 N, what is the maximum speed the ball can attain before the cord breaks? mFrrvar2Centripetal acceleration:rFWhen does the string break?When the centripetal force is greater than the sustainable tension.Trvm 2Calculate the tension of the cord when speed of the ball is 5.00m/s. NrvmT 33.85.100.5500.022 smmTrv /2.12500.05.10.50rmarvm2TWednesday, Feb. 18, 2004 7 PHYS 1443-501, Spring 2004Dr. Andrew BrandtExample of Banked Highway(a) For a car traveling with speed v around a curve of radius r, determine a formula for the angle at which a road should be banked so that no friction is required to keep the car from skidding. rmvn2sin yFxFsmhrkmv /14/50 x comp.y comp.xyrmansincosmgnq=0 mgncosrmvmgmgn2tancossinsin grv2tan 4.08.95014tan2rmvn2sin0mgn cos(b) What is this angle for an expressway off-ramp curve of radius 50m at a design speed of 50km/h?
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