Lecture 9Friction in a viscous medium Drag Force QuantifiedNewton’s Third Law:Force Pairs vs. Free Body DiagramsForces just on a single body (1st and 2nd Laws only)Force Pairs (3rd Law)Example (non-contact)Note on Gravitational ForcesSlide 9A conceptual question: A flying bird in a cage3rd Law : Static Friction with a bicycle wheelStatic Friction with a bicycle wheelExercise Newton’s Third LawExercise Newton’s 3rd LawExercise Newton’s 3rd Law SolutionExercise Newton’s 3rd LawForce pairs on an Inclined planeSlide 18Example: Friction and MotionExample SolutionSlide 21Slide 22Slide 23RecapPhysics 207: Lecture 9, Pg 1Lecture 9GoalsGoals Describe Friction in Air (Ch. 6), (not on 1st Exam) Differentiate between Newton’s 1st, 2nd and 3rd Laws Use Newton’s 3rd Law in problem solving1st Exam Thurs., Oct. 6th from 7:15-8:45 PM Chapters 1-6 & 7(“light”, direct applications of the third law)Rooms: 2103 (302, 303, 306, 309, 310, 313) 2141 (304, 307, 308, 312) , 2223 (311) Chamberlin Hall (plus quiet room)Physics 207: Lecture 9, Pg 2Friction in a viscous mediumDrag Force QuantifiedWith a cross sectional area, A (in m2), coefficient of drag of 1.0 (most objects), sea-level density of air, and velocity, v (m/s), the drag force is:D = ½ C A v2 c A v2 in Newtons c = ¼ kg/m3 In falling, when D = mg, then at terminal velocityExample: Bicycling at 10 m/s (22 m.p.h.), with projected area of 0.5 m2 exerts a force of ~30 Newtons At low speeds air drag is proportional to v but at high speeds it is v2 Minimizing drag is often importantPhysics 207: Lecture 9, Pg 3Newton’s Third Law:If object 1 exerts a force on object 2 (F2,1 ) then object 2 exerts an equal and opposite force on object 1 (F1,2)F1,2 = -F2,1IMPORTANT: Newton’s 3rd law concerns force pairs whichact on two different objects (not on the same object) ! For every “action” there is an equal and opposite “reaction”Physics 207: Lecture 9, Pg 4Force Pairs vs. Free Body DiagramsConsider the following two cases (a falling ball and ball on table),Compare and contrast Free Body Diagram andAction-Reaction Force Pair sketchPhysics 207: Lecture 9, Pg 5Forces just on a single body (1st and 2nd Laws only)mgmgFB,T= NBall FallsFor Static SituationN = mgPhysics 207: Lecture 9, Pg 6Force Pairs (3rd Law)1st and 2nd Laws Free-body diagram Relates force to acceleration3rd Law Action/reaction pairsShows how forces act between objectsFB,E = -mgFB,T= NFE,B = mgFB,E = -mgFE,B = mgFT,B= -NPhysics 207: Lecture 9, Pg 7Example (non-contact)Consider the forces on an object undergoing projectile motionFB,E = - mB gEARTHFE,B = mB gFB,E = - mB gFE,B = mB gQuestion: By how much does g change at an altitude of 40 miles? (Radius of the Earth ~4000 mi)Physics 207: Lecture 9, Pg 8Note on Gravitational ForcesNewton also recognized that gravity is an attractive, long-range force between any two objects. When two objects with masses m1 and m2 are separated by distance r, each object “pulls” on the other with a force given by Newton’s law of gravity, as follows:Physics 207: Lecture 9, Pg 9Example (non-contact)Consider the force on a satellite undergoing projectile motion 40 km above the surface of the earth:FB,E = - mB gEARTHFE,B = mB gFB,E = - mB gFE,B = mB gCompare: g = G m2 / 40002 g’ = G m2 / (4000+40)2 g’ / g = 40002 / (4000+40)2 = 0.98Physics 207: Lecture 9, Pg 10A conceptual question: A flying bird in a 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?Follow up question:So, what is holding the airplane up in the sky?Physics 207: Lecture 9, Pg 113rd Law : Static Friction with a bicycle wheelYou are pedaling hard and the bicycle is speeding up.What is the direction of the frictional force?You are breaking and the bicycle is slowing downWhat is the direction of the frictional force?Physics 207: Lecture 9, Pg 12Static Friction with a bicycle wheelYou are pedaling hard and the bicycle is speeding up.What is the direction of the frictional force?Hint…you are accelerating to the righta = F / mFfriction, on B from E is to the rightFfriction, on E from,B is to the leftPhysics 207: Lecture 9, Pg 13Exercise Newton’s Third LawA. greater thanB. equal to C. less thanA fly is deformed by hitting the windshield of a speeding bus. vThe force exerted by the bus on the fly is,that exerted by the fly on the bus.Physics 207: Lecture 9, Pg 14ExerciseNewton’s 3rd LawA. greater thanB. equal to C. less thanA fly is deformed by hitting the windshield of a speeding bus. vThe magnitude of the acceleration, due to this collision, of the bus isthat of the fly.Same scenario but now we examine the accelerationsPhysics 207: Lecture 9, Pg 15Exercise Newton’s 3rd LawSolutionBy Newton’s third law these two forces form an interaction pair which are equal (but in opposing directions). However, by Newton’s second law Fnet = ma or a = Fnet/m.So Fb, f = -Ff, b = F0but |abus | = |F0 / mbus | << | afly | = | F0/mfly |Thus the forces are the same Answer for acceleration is (C)Physics 207: Lecture 9, Pg 16Exercise Newton’s 3rd LawA. 2B. 4C. 6D. Something elseabTwo blocks are being pushed by a finger on a horizontal frictionless floor. How many action-reaction force pairs are present in this exercise?Physics 207: Lecture 9, Pg 17Force pairs on an Inclined planeForces on the block (static case)NormalForceFriction Forcef= N xyForces on the plane by blockPhysics 207: Lecture 9, Pg 18Force pairs on an Inclined planeForces on the block (sliding case, no friction)NormalForcexyJust one force on the plane by blockso if plane is to remain stationary these two components must be offset by other force pairs(N cos and N sin along vertical and horizontal)Physics 207: Lecture 9, Pg 19 Example: Friction and Motion A box of mass m1 = 1 kg is being pulled by a horizontal string having tension T = 40 N. It slides with friction (k= 0.5) on top of a second box having mass m2 = 2 kg, which in turn slides on a smooth (frictionless) surface.(g is said to be 10 m/s2) What is the
View Full Document
Unlocking...