Page 1Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 1Lecture 6Chapter 5 and 6 goals:Chapter 5 and 6 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 IRF is and how it relates to Newton’s LawsAssignment: HW3, (Chapters 4 & 5, due 2/11, Wednesday)Finish reading Chapter 6Exam 1 Wed, Feb. 18 from 7:15-8:45 PM Chapters 1-7Physics 207: Lecture 6, Pg 2Relative motion and frames of reference Reference frame S is stationary Reference frame S’ is moving at voThis also means that S moves at – vorelative to S’ Define time t = 0 as that time when the origins coincidePhysics 207: Lecture 6, Pg 3Relative Velocity The positions, r and r’, as seen from the two reference frames are related through the velocity, vo, where vois velocity of the r’ reference frame relative to r r’ = r – vo∆t The derivative of the position equation will give the velocity equation v’ = v – vo These are called the Galilean transformation equations Reference frames that move with “constant velocity” (i.e., at constant speed in a straight line) are defined to be inertial reference frames (IRF); anyone in an IRF sees the sameacceleration of a particle moving along a trajectory. a’ = a (dvo/ dt = 0)Physics 207: Lecture 6, Pg 4Central concept for problem solving: “x” and “y”components of motion treated independently. Example: Man on cart tosses a ball straight up in the air. You can view the trajectory from two reference frames:Reference frame on the ground.Reference frame on the moving cart.y(t) motion governed by 1) a = -g y2) vy= v0y– g ∆t3) y = y0+ v0y– g ∆t2/2x motion: x = vxtNet motion: R = x(t) i + y(t) j (vector)Physics 207: Lecture 6, Pg 5What causes motion?(Actually changes in motion)What are forces ?What kinds of forces are there ?How are forces and changes in motion related ?Physics 207: Lecture 6, Pg 6Newton’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 7IRFs 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 8Newton’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)Physics 207: Lecture 6, Pg 9Example 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 10Contact (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 6, Pg 11No 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 12No 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 3Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 13A 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 14Friction... Friction is caused by the “microscopic” interactions between the two surfaces:Physics 207: Lecture 6, Pg 15Friction... Force of friction acts to oppose motion: Parallel to a surface Perpendicular to a NNormal force.maFFffFmggNNiij j Physics 207: Lecture 6, Pg 16Static 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 6, Pg 17Important 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 18Pushing 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 4Physics 207 – Lecture 6Physics 207: Lecture 6, Pg 19Examples of Contact Forces:A spring can pushPhysics 207: Lecture 6, Pg 20A spring can pullPhysics 207: Lecture 6, Pg 21Ropes provide tension (a pull)In physics we often use a “massless” rope with opposing tensions of equal magnitudePhysics 207: Lecture 6, Pg 22Forces 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 6, Pg 23Free 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
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