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UT Arlington PHYS 1443 - Lecture Notes

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Slide 1AnnouncementsExample for Using Newton’s LawsForces of FrictionExample w/ FrictionNewton’s Second Law & Uniform Circular MotionExample of Uniform Circular MotionExample of Banked HighwayForces in Non-uniform Circular MotionExample for Non-Uniform Circular MotionMotion in Resistive ForcesResistive Force Proportional to SpeedWednesday, Sept. 22, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu11. Forces of Friction2. Uniform and Non-uniform Circular Motions3. Resistive Forces and Terminal Velocity4. Newton’s Law of Universal Gravitation5. Kepler’s LawsPHYS 1443 – Section 003Lecture #9Wednesday, Sept. 22, 2004Dr. Jaehoon YuRemember the first term exam next Monday, Sept. 27!!Homework #6 due at 1pm next Wednesday, Oct. 6!!Wednesday, Sept. 22, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu2Announcements•Quiz Results–Class Average: 3.6/8–Top score: 7–We have a few more quizzes through the semester•Remember the 1st term exam, Monday, Sept. 27–1:00 – 2:20pm in class–Covers Chapters 1 - 6.4 –Mixture of multiple choice and free style problems–PLEASE DO NOT Miss the exam!!!!Wednesday, Sept. 22, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu3Example for Using Newton’s LawsA traffic light weighing 125 N hangs from a cable tied to two other cables fastened to a support. The upper cables make angles of 37.0o and 53.0o with the horizontal. Find the tension in the three cables. F =urFree-bodyDiagram53o37oxyT137oT253oT3( ) ( )1 2sin 37 sin 53T T mg+ - =o o   053cos37cos21TT1T\ =    NTT 12525.137sin754.053sin222100 ; T N=031iiixxTF031iiiyyTFNewton’s 2nd lawx-comp. of net forcey-comp. of net force0( )( )2cos 53cos 37T =oo20.754T1 2 0.754 75.4T T N= =1 2 3T T T+ + =ur ur urma =r0Wednesday, Sept. 22, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu4Forces of FrictionnfssResistive force exerted on a moving object due to viscosity or other types frictional property 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 movementnfkkThese forces are either proportional to the velocity or the normal force.Empirical Formula What does this formula tell you? Frictional force increases till it reaches the limit!!Beyond the limit, the object moves, and there is NO MORE static friction but kinetic friction takes it over.Which direction does kinetic friction apply?Opposite to the motion!Wednesday, Sept. 22, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu5Example 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-bodyDiagramxyMaFgnnF= -Mgfs=knyFxFsNet forcex comp.y comp.sfnxyaMsgfnF sgxfFsfMgsin0nscMgsinyMagyFncMgncos0gyFcMgcosnMgcsinccMgMgcossinctanWednesday, Sept. 22, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu6Newton’s Second Law & Uniform Circular Motionrvar2The centripetal acceleration is always perpendicular to velocity vector, v, for uniform circular motion.The force that causes the centripetal acceleration acts toward the center of the circular path 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 the tangential direction to the circle.rmarvm2Wednesday, Sept. 22, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu7Example 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? mFrra =Centripetal acceleration:rFWhen does the string break?when the centripetal force is greater than the sustainable tension.2vmr=Calculate the tension of the cord when speed of the ball is 5.00m/s.T =v =rmarvm2TTTrm=( )50.0 1.512.2 /0.500m s�=2vmr=( )( )25.000.500 8.331.5N� =2vrWednesday, Sept. 22, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu8Example 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. 2sinNmvFrq =yFxFsmhrkmv /14/50 x comp.y comp.xysinN rF maq - =sinNmgFq=0cosNF mgq - =sinNF q =grv2tan  4.08.95014tan22sinNmvFrq - =0cosNF mgq =(b) What is this angle for an expressway off-ramp curve of radius 50m at a design speed of 50km/h?  o224.0tan1sincosmg qq=tanmg q =2mvrWednesday, Sept. 22, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu9Forces in Non-uniform Circular MotionThe object has both tangential and radial accelerations.What does this statement mean?The object is moving under both tangential and radial forces.FrFtFF =urThese forces cause not only the velocity but also the speed of the ball to change. The object undergoes a curved motion under the absence of constraints, such as a string. a =What is the magnitude of the net acceleration?rF +urtFur2 2r ta a+Wednesday, Sept. 22, 2004 PHYS 1443-003, Fall 2004Dr. Jaehoon Yu10Example for Non-Uniform Circular MotionA ball of mass m is attached to the end of a cord of length R. The ball is moving in a vertical circle. Determine the tension of the cord at any instant when the speed of the ball is v and the cord makes an angle with vertical. TmWhat are the forces involved in this motion?tF•The gravitational force Fg •The radial force, T, providing tension. RFg=mgAt what angles the tension becomes maximum and minimum. What are the tensions?singatrFcos2gRvmTtangential comp.Radial comp.sinmgtmacosmgTrmaRvm2Wednesday, Sept. 22, 2004 PHYS 1443-003, Fall


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UT Arlington PHYS 1443 - Lecture Notes

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