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UW-Madison PHYSICS 207 - PHYSICS 207 Lecture Notes

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Physics 207, Lecture 8, Oct. 2Non uniform Circular MotionExample Gravity, Normal Forces etc.Lecture 8, Exercise 1 Gravity, Normal Forces etc.Loop-the-loop 1Loop-the-loop 1Loop-the-loop 2Loop-the-loop 3Lecture 8, Exercise 2 Non uniform Circular MotionAccelerated Reference Frames: The AccelerometerSlide 11Slide 12Lecture 8, Exercise 3 Accelerated Reference FramesLecture 7, Exercise 3 Accelerated Reference FramesAir Resistance and DragAristotle's Laws of MotionDrag Force QuantifiedAir Drag in Auto Design: D = (1/2) C  A v2“Free” FallTrajectories with Air ResistanceRecappingProblem solving…Example with pulleyLecture 8, Exercise 4Example Problem 5.40 from SerwayPhysics 207: Lecture 8, Pg 1Physics 207, Physics 207, Lecture 8, Oct. 2Lecture 8, Oct. 2Agenda:Agenda:Assignment:Assignment:WebAssign Problem Set 3 due Oct. 3, Tuesday 11:59 PMWebAssign Problem Set 3 due Oct. 3, Tuesday 11:59 PMMidTerm Thurs., Oct. 5, Chapters 1-6, 90 minutes, 7:15-8:45 PMMidTerm Thurs., Oct. 5, Chapters 1-6, 90 minutes, 7:15-8:45 PMNOTE: Assigned Rooms are 105 and 113 PsychologyNOTE: Assigned Rooms are 105 and 113 Psychology •Chapter 6 (Circular Motion and Other Applications) Uniform and non-uniform circular motion Accelerated Frames Resistive Forces•Problem Solving and Review for MidTerm IPhysics 207: Lecture 8, Pg 2Non uniform Circular MotionNon uniform Circular MotionEarlier we saw that for an object movingin a circle with non uniform speed then a = ar + at (radial and tangential)aratWhat are Fr and Ft ?mar and matPhysics 207: Lecture 8, Pg 3ExampleExampleGravity, Normal Forces etc.Gravity, Normal Forces etc.Consider a person on a swing: When is the tension on the rope largest ? And at that point is it :(A) greater than(B) the same as(C) less thanthe force due to gravity acting on the personActive FigurePhysics 207: Lecture 8, Pg 4Lecture 8, Lecture 8, Exercise 1Exercise 1Gravity, Normal Forces etc.Gravity, Normal Forces etc.At the bottom of the swings and is it (A) greater thanthe force due to gravity acting on the personvmgTFc = m ac = m v2 / r = T - mgT = mg + m v2 / rmgTFc = m 02 / r = 0 = T – mg cos FT = m aT = mg sin  Physics 207: Lecture 8, Pg 5A match box car is going to do a loop-the-loop of radius r. What must be its minimum speed, v, at the top so that it can manage the loop successfully ?Loop-the-loop 1 Loop-the-loop 1Physics 207: Lecture 8, Pg 6To navigate the top of the circle its tangential velocity, v, must be such that its centripetal acceleration at least equals the force due to gravity. At this point N, the normal force, goes to zero. Loop-the-loop 1Loop-the-loop 1Fc = - ma = - mg = - mv2/rv = (gr)1/2mgvPhysics 207: Lecture 8, Pg 7Once again the the box car is going to execute a loop-the-loop. What must be its minimum speed at the bottom so that it can make the loop successfully?This is a difficult problem to solve using just forces. We will skip it now and revisit it using energy considerations in Ch. 9.Loop-the-loop 2Loop-the-loop 2Physics 207: Lecture 8, Pg 8The match box car is going to do a loop the loop. If the speed at the bottom is vB, what is the normal force, N, at that point?Hint: The car is constrained to the track. Loop-the-loop 3Loop-the-loop 3mgvNFc = ma = mvB2/r = N - mgN = mvB2/r + mgPhysics 207: Lecture 8, Pg 9We construct a roller coaster designed so that when one rider alone becomes weightless at the top and has a speed v1. Now two additional passenger get in so that the total weight of the car (at rest) and people doubles. How fast must the car go so we are still weightless at the top ?Normal force is zero.Lecture 8, Lecture 8, Exercise 2Exercise 2Non uniform Circular MotionNon uniform Circular Motion(A) 1/2 v1(B) v1 (C) 2 v1 (D) 4 v1v Fc = -2ma = -2mv2/r = -2mg (B) v = (gr)1/2 = v1Physics 207: Lecture 8, Pg 10Accelerated Reference Frames:Accelerated Reference Frames:The AccelerometerThe AccelerometerYour first job is with Ford. You are working on a project to design an accelerometer. The inner workings of this gadget consist of a weight of mass m that is hung inside a box that is attached to the ceiling of a car. You design the device with a very light string so that you can mathematically ignore it. The idea is that the angle the string makes with the vertical, , is determined by the car’s acceleration. Your preliminary task is to think about calibration of the accelerometer when the car travels on a flat road.What is the car’s acceleration a when the hanging mass makes an angle with the vertical?See example 6-9: Train CarSee text: 6-3Physics 207: Lecture 8, Pg 11Accelerated Reference Frames:Accelerated Reference Frames:The AccelerometerThe Accelerometerai i See text: 6-31We need to solve for the angle the plum bob makes with respect to vertical. We will solve by using Newton’s Second Law and checking x and y components.Physics 207: Lecture 8, Pg 12Accelerated Reference Frames:Accelerated Reference Frames:The AccelerometerThe Accelerometerai i See text: 6-3mgTx-dir Fx = -ma = -T sin y-dir Fy = 0 = T cos mgT = mg / cos a = T sinm = g tan Physics 207: Lecture 8, Pg 13Lecture 8,Lecture 8, Exercise 3Exercise 3Accelerated Reference FramesAccelerated Reference FramesYou are a passenger in a car and not wearing your seatbelt. Without increasing or decreasing speed, the car makes a sharp left turn, and you find yourself colliding with the right-hand door. Which is a correct description of the situation ?(A) Before and after the collision there is a rightward force pushing you into the door.(B) Starting at the time of the collision, the door exerts a leftward force on you.(C) Both of the above.(D) Neither of the above.Physics 207: Lecture 8, Pg 14Lecture 7,Lecture 7, ExerciseExercise 33Accelerated Reference FramesAccelerated Reference FramesNewton’s first law says that you will continue to travel with a constant velocity as long as there are no forces acting on you. This is also known as inertia. As you try to continue to travel straight, you collide with the car door which is starting to accelerate leftward. This contact force forces your body to accelerate and turn with the car.(B) Starting at the time of the collision, the door exerts a leftward force on you.Active FigurePhysics 207: Lecture 8, Pg 15Air Resistance and Drag Air Resistance and Drag So far we’ve “neglected air resistance” in physics Can be


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UW-Madison PHYSICS 207 - PHYSICS 207 Lecture Notes

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