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UW-Madison PHYSICS 207 - Lecture 7 Notes

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Lecture 7Identifying Forces: Non-contactContact (i.e., normal) ForcesNo net force  No accelerationSlide 5A special contact force: FrictionFriction...Slide 8Static Friction with a bicycle wheelImportant notesPushing and Pulling ForcesExamples of Contact Forces: A spring can pushA spring can pullRopes provide tension (a pull)Forces at different anglesFree Body DiagramSlide 17Slide 18Exercise, Newton’s 2nd LawMassInertia and MassExercise Newton’s 2nd LawExercise Newton’s 2nd LawMoving forces aroundScale ProblemSlide 31Static and Kinetic FrictionFriction: Static frictionStatic friction, at maximum (just before slipping)Kinetic or Sliding friction (fk < fs)Sliding Friction: QuantitativelyCoefficients of FrictionAn experimentA 2nd experimentAn experiment (with a ≠ 0)RecapPhysics 207: Lecture 7, Pg 1Lecture 7Goals:Goals: Solve 1D and 2D problems with forces in equilibrium and non-equilibrium (i.e., acceleration) using Newton’ 1st and 2nd laws. Distinguish static and kinetic coefficients of friction Differentiate between Newton’s 1st, 2nd and 3rd LawsAssignment: HW4, (Chapters 6 & 7 (1st part)due 2/17, 9 am, Wednesday)For Thursday, Read Chapter 7 1st Exam Thursday, Feb. 17 from 7:15-8:45 PM Chapters 1-7Physics 207: Lecture 7, Pg 2Identifying Forces: Non-contactAll objects having mass exhibit a mutually attractive force (i.e., gravity) that is distance dependentAt the Earth’s surface this variation is small so little “g” (the associated acceleration) is typically set to 9.80 or 10. m/s2 FB,GPhysics 207: Lecture 7, Pg 3Contact (i.e., normal) ForcesCertain forces act to keep an object in place. These have what ever force needed to balance all others (until a breaking point).FB,TPhysics 207: Lecture 7, Pg 4No net force  No accelerationFB,T Normal force is always  to a surface000netyxFFamFFFB,G(Force vectors are not always drawn at contact points)mgNNmgFy 0yPhysics 207: Lecture 7, Pg 5No net force  No acceleration0net amFFIf zero velocity then “static equilibrium”If non-zero velocity then “dynamic equilibrium”This label, static vs. dynamic, is observer dependent Forces are vectors321netFFFamFFPhysics 207: Lecture 7, Pg 6A special contact force: FrictionWhat does it do? It opposes motion (velocity, actual or that which would occur if friction were absent!)How do we characterize this in terms we have learned? Friction results in a force in a direction opposite to the direction of motion (actual or, if static, then “inferred”)!maFFAPPLIEDffFRICTIONmggNNii j jPhysics 207: Lecture 7, Pg 7Friction...Friction is caused by the “microscopic” interactions between the two surfaces:Physics 207: Lecture 7, Pg 8Friction...Force of friction acts to oppose motion: Parallel to a surface Perpendicular to a NNormal force.maFFffFmggNNii j jPhysics 207: Lecture 7, Pg 9Static Friction with a bicycle wheelYou 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 7, Pg 10Important notesMany contact forces are conditional and, more importantly, they are not necessarily constantWe have a general notion of forces is from everyday life.In physics the definition must be precise. A force is an action which causes a body to accelerate.(Newton’s Second Law)On a microscopic level, all forces are non-contactPhysics 207: Lecture 7, Pg 11Pushing and Pulling ForcesA rope is an example of something that can pullYou arm is an example of an object that can push or pushPhysics 207: Lecture 7, Pg 12Examples of Contact Forces:A spring can pushPhysics 207: Lecture 7, Pg 13A spring can pullPhysics 207: Lecture 7, Pg 14Ropes provide tension (a pull)In physics we often use a “massless” rope with opposing tensions of equal magnitudePhysics 207: Lecture 7, Pg 15Forces at different anglesCase 1Case 2FmgNCase1: Downward angled force with frictionCase 2: Upwards angled force with frictionCases 3,4: Up against the wallQuestions: Does it slide? What happens to the normal force?What happens to the frictional force?mgCases 3, 4mgNNFFffffffPhysics 207: Lecture 7, Pg 16Free Body DiagramA heavy sign is hung between two poles by a rope at each corner extending to the poles.Eat at Bucky’sA hanging sign is an example of static equilibrium (depends on observer)What are the forces on the sign and how are they related if the sign is stationary (or moving with constant velocity) in an inertial reference frame ?Physics 207: Lecture 7, Pg 17Free Body DiagramStep two: Sketch in force vectorsStep three: Apply Newton’s 2nd Law (Resolve vectors into appropriate components)mgT1T2Eat at Bucky’sT1T2mgStep one: Define the systemPhysics 207: Lecture 7, Pg 18Free Body DiagramEat at Bucky’sT1T2mgVertical : y-direction 0 = -mg + T1 sin1 + T2 sin2Horizontal : x-direction 0 = -T1 cos1 + T2 cos2Physics 207: Lecture 7, Pg 19Exercise, Newton’s 2nd LawA. P + C < W B. P + C > WC. P = CD. P + C = WA woman is straining to lift a large crate, without success. It is too heavy. We denote the forces on the crate as follows: P is the upward force being exerted on the crate by the personC is the contact or normal force on the crate by the floor, and W is the weight (force of the earth on the crate). Which of following relationships between these forces is true, while the person is trying unsuccessfully to lift the crate? (Note: force up is positive & down is negative)Physics 207: Lecture 7, Pg 20MassWe have an idea of what mass is from everyday life.In physics: Mass (in Phys 207) is a quantity that specifies how much inertia an object has (i.e. a scalar that relates force to acceleration)(Newton’s Second Law)Mass is an inherent property of an object.Mass and weight are different quantities; weight is usually the magnitude of a gravitational (non-contact) force. “Pound” (lb) is a definition of weight (i.e., a force), not a mass!Physics 207: Lecture 7, Pg 21Inertia and MassThe tendency of an object to resist any attempt to change its velocity is called InertiaMass is that property of an object that specifies how much resistance an object exhibits to changes in its velocity


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UW-Madison PHYSICS 207 - Lecture 7 Notes

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