Lecture 9Textbook ChaptersThe flying bird in the cageExample with pulleySlide 5ExampleAnother ExampleExample Wedge with frictionSlide 9Slide 10Slide 11Example Another settingAnother example with a pulleyProblem recast as 1D motionSlide 15Chapter 2Slide 18Chapter 3Slide 20Chapter 4Slide 22Chapter 5Chapter 5 & 6Chapter 6Chapter 7Slide 27Short word problemsConceptual ProblemSlide 30Graphing problemSlide 32Slide 33Slide 34Sample ProblemSlide 37Another question to ponderSlide 39Physics 207: Lecture 9, Pg 1Lecture 9Today:Today: Review sessionAssignment: For Thursday, Read Chapter 8, first four sectionsExam Wed., Feb. 18th from 7:15-8:45 PM Chapters 1-7One 8½ X 11 note sheet and a calculator (for trig.)Place: Room 2103: All SectionsPhysics 207: Lecture 9, Pg 2Textbook ChaptersChapter 1 Concept of MotionChapter 2 1D KinematicsChapter 3 Vector and Coordinate SystemsChapter 4 Dynamics I, Two-dimensional motionChapter 5 Forces and Free Body DiagramsChapter 6 Force and Newton’s 1st and 2nd LawsChapter 7 Newton’s 3rd Law Exam will reflect most key points (but not all) ~30% of the exam will be more conceptual ~70% of the exam is problem solvingPhysics 207: Lecture 9, Pg 3The flying bird in the cageYou have a bird in a cage that is resting on your upward turned palm. The cage is completely sealed to the outside (at least while we run the experiment!). The bird is initially sitting at rest on the perch. It decides it needs a bit of exercise and starts to fly. Question: How does the weight of the cage plus bird vary when the bird is flying up, when the bird is flying sideways, when the bird is flying down?So, what is holding the airplane up in the sky?Physics 207: Lecture 9, Pg 4Example with pulleyA mass M is held in place by a force F. Find the tension in each segment of the massless ropes and the magnitude of F. Assume the pulleys are massless and frictionless.•The action of a massless frictionless pulley is to change the direction of a tension.•This is an example of static equilibrium.MT5T4T3T2T1FPhysics 207: Lecture 9, Pg 5Example with pulleyA mass M is held in place by a force F. Find the tension in each segment of the rope and the magnitude of F. Assume the pulleys are massless and frictionless. Assume the rope is massless.•The action of a massless frictionless pulley is to change the direction of a tension.•Here F = T1 = T2 = T3 = T•Equilibrium means F = 0 for x, y & z•For example: y-dir ma = 0 = T2 + T3 – T5 and ma = 0 = T5 – Mg •So T5 = Mg = T2 + T3 = 2 F T = Mg/2 MT5T4T3T2T1FPhysics 207: Lecture 9, Pg 6ExampleThe velocity of an object as a function of time is shown in the graph at right. Which graph below best represents the net force vs time relationship for this object? (E)Physics 207: Lecture 9, Pg 7Another ExampleA 200 kg truck accelerates eastwards on a horizontal road in response to a gradually increasing frictional force from the ground. There is an unsecured 50 kg block sitting on the truck bed liner. There is friction between the block and the bed liner. An accelerometer is mounted in the truck. The block accelerates with the truck until the acceleration reaches 10 m/s2. At that instant the block begins to slide and the truck’s accelerometer now reports a value of 11 m/s2. What are the coefficients of static and kinetic friction? S=1.0 k=0.60accelerationtime1110Physics 207: Lecture 9, Pg 8ExampleWedge with friction A mass m slides with friction down a wedge of angle at constant velocity. The wedge sits at rest on a frictionless surface and abuts a wall. What is the magnitude of the force of the wall on the block?mvmgNfkFBD blockPhysics 207: Lecture 9, Pg 9Example Wedge with friction A mass m slides with friction down a wedge of mass M & angle at constant velocity. The wedge sits at rest on a frictionless surface and abuts a wall. What is the magnitude of the force of the wall on the block?mvmgNfkFBD blockFBD wedge-N-fkMgFwFF3rd LawPhysics 207: Lecture 9, Pg 10Example Wedge with friction A mass m slides with friction down a wedge of mass M & angle at constant velocity. The wedge sits at rest on a frictionless surface and abuts a wall. What is the magnitude of the force of the wall on the block?mgNfkFBD blockx-dir: Fx = 0 = -fk + mg sin fk = mg sin y-dir: Fy = 0 = N - mg cos N = mg cos yxPhysics 207: Lecture 9, Pg 11Example Wedge with friction A mass m slides with friction down a wedge of mass M & angle at constant velocity. The wedge sits at rest on a frictionless surface and abuts a wall. What is the magnitude of the force of the wall on the block?Notice that mg cos sin mg cos sin Force wall = 0 But there are faster ways.FBD wedgemg cos MgFwFFmg sin mg cos sin mg cos sin Physics 207: Lecture 9, Pg 12ExampleAnother setting Three blocks are connected on the table as shown. The table has a coefficient of kinetic friction of K=0.40, the masses are m1 = 4.0 kg, m2 = 1.0 kg and m3 = 2.0 kg. (A) What is the magnitude and direction of acceleration on the three blocks ?(B) What is the tension on the two cords ?m1T1m2m3Physics 207: Lecture 9, Pg 13Another example with a pulleyThree blocks are connected on the table as shown. The table has a coefficient of kinetic friction of K=0.40, the masses are m1 = 4.0 kg, m2 = 1.0 kg and m3 = 2.0 kg. (A) FBD (except for friction) (B) So what about friction ?m1T1m2m3m2gNm3gm1gT3T1Physics 207: Lecture 9, Pg 14Problem recast as 1D motionThree blocks are connected on the table as shown. The center table has a coefficient of kinetic friction of K=0.40, the masses are m1 = 4.0 kg, m2 = 1.0 kg and m3 = 2.0 kg. m1m2m3m2gNm3gm1gT3T1frictionlessfrictionlessm1g > m3g and m1g > (km2g + m3g) and friction opposes motion (starting with v = 0)so ff is to the right and a is to the left (negative)ffPhysics 207: Lecture 9, Pg 15Problem recast as 1D motionThree blocks are connected on the table as shown. The center table has a coefficient of kinetic friction of K=0.40, the masses are m1 = 4.0 kg, m2 = 1.0 kg and m3 = 2.0 kg. m1m2m3m2gNm3gm1gT3T1frictionlessfrictionlessx-dir: 1. Fx = m2a = k m2g - T1 + T3 m3a = m3g - T3 m1a = m1g + T1 Add all three: (m1 + m2 + m3) a = k m2gm3g – m1g
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