Page 1Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 1Physics 207, Lecture 6, Sept. 22Goals:Goals: Recognize different types of forces and know how they act on an object in a particle representation Identify forces and draw a Free Body Diagram Solve 1D and 2D problems with forces in equilibrium and non-equilibrium (i.e., acceleration) using Newton’ 1stand 2ndlaws. Know what an IRD is and how it relates to Newton’s LawsAssignment: HW3, (Chapters 4 & 5, due 9/25, Wednesday)Read up through Chapter 7, Section 51stExam Thursday, Oct. 2ndfrom 7:15-8:45 PM Chapters 1-7Physics 207: Lecture 6, Pg 2Newton’s First Law and IRFsAn object subject to no external forces moves with constant velocity if viewed from aninertial reference frame (IRF)inertial reference frame (IRF).If no net force acting on an object, there is no acceleration. The above statement can be used to define inertial reference frames.Page 2Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 3IRFs An IRF is a reference frame that is not accelerating (or rotating) with respect to the “fixed stars”. If one IRF exists, infinitely many exist since they are related by any arbitrary constant velocity vector! In many cases (i.e., Chapters 5, 6 & 7) the surface of the Earth may be viewed as an IRFPhysics 207: Lecture 6, Pg 4Newton’s Second LawThe acceleration of an object is directly proportional to the net force acting upon it. The constant of proportionality is the mass. This expression is vector expression: Fx, Fy, Fz UnitsThe metric unit of force is kg m/s2= Newtons (N)The English unit of force is Pounds (lb)Page 3Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 5Example Non-contact ForcesAll 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/s2FB,GPhysics 207: Lecture 6, Pg 6Contact (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,TPage 4Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 7No net force No accelerationFB,T Normal force is always ⊥ to a surface000net=∑=∑===∑yxFFamFFrrrFB,G(Force vectors are not always drawn at contact points)mgNNmgFy==+−=∑0yPhysics 207: Lecture 6, Pg 8No net force No acceleration0net===∑amFFrrr If zero velocity then “static equilibrium” If non-zero velocity then “dynamic equilibrium” This label depends on the observer Forces are vectorsKrrrrrr+++==≡∑321netFFFamFFPage 5Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 9A 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”)!maFFAPPLIEDffFRICTIONmggNNiij j Physics 207: Lecture 6, Pg 10Friction... Friction is caused by the “microscopic” interactions between the two surfaces:Page 6Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 11Friction... Force of friction acts to oppose motion: Parallel to a surface Perpendicular to a NNormal force.maFFffFmggNNiij j Physics 207: Lecture 6, Pg 12Static 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?Page 7Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 13Important 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 6, Pg 14Pushing 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 pushPage 8Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 15Examples of Contact Forces:A spring can pushPhysics 207: Lecture 6, Pg 16A spring can pullPage 9Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 17Ropes provide tension (a pull)In physics we often use a “massless” rope with opposing tensions of equal magnitudePhysics 207: Lecture 6, Pg 18Forces 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, 4mgNNFFffffffPage 10Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 19Free 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 6, Pg 20Free Body DiagramStep two: Sketch in force vectorsStep three: Apply Newton’s 2ndLaw (Resolve vectors into appropriate components)θ2mgθ1T1T2Eat at Bucky’sθ1θ2T1T2mgStep one: Define the systemPage 11Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 21Free Body DiagramEat at Bucky’sθ1θ2T1T2mgVertical :y-direction 0 = -mg + T1 sinθ1+ T2 sinθ2Horizontal :x-direction 0 = -T1 cosθ1+ T2 cosθ2Physics 207: Lecture 6, Pg 22Exercise, Newton’s 2ndLawA. P + C < WB. P + C > WC. P = CD. P + C = WA woman is strainingto lifta large crate,withoutsuccess. Itistooheavy. We denotetheforces onthe crate asfollows:P is the upward force being exerted on the crate by the personC is the contact force on the crate by the floor, and W is the weight (force of the earth on the crate). Whichof followingrelationships betweentheseforces istrue,whilethe person istrying unsuccessfullyto lift thecrate? (Note:force up is positive & down is negative)Page 12Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 23Mass 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
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