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Physics I 95.141 LECTURE 8 9/29/10 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Exam Prep Problem • A 5kg block (A) sits on an inclined plane tilted at an angle of 30º. It is attached via a massless cord to a block of mass 2kg (B) lying on a flat surface. Ignore friction. – (10pts) Draw a free body diagram for each block (include coordinate system). – (8pts) What are the magnitude of the Normal Forces on each block? – (10pts) What is the acceleration of the blocks? – (7pts) What is the tension in the cord? B A θ =30° 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Exam Prep Problem • A 5kg block (A) sits on an inclined plane tilted at an angle of 30º. It is attached via a massless cord to a block of mass 2kg (B) lying on a flat surface. Ignore friction. – (10pts) Draw a free body diagram for each block (include coordinate system). 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Exam Prep Problem • A 5kg block (A) sits on an inclined plane tilted at an angle of 30º. It is attached via a massless cord to a block of mass 2kg (B) lying on a flat surface. Ignore friction. – (8pts) What are the magnitude of the Normal Forces on each block? 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Exam Prep Problem • A 5kg block (A) sits on an inclined plane tilted at an angle of 30º. It is attached via a massless cord to a block of mass 2kg (B) lying on a flat surface. Ignore friction. – (5pts) What is the acceleration of the blocks? 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Exam Prep Problem • A 5kg block (A) sits on an inclined plane tilted at an angle of 30º. It is attached via a massless cord to a block of mass 2kg (B) lying on a flat surface. Ignore friction. – (4pts) What is the tension in the cord? 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Common Mistakes • Orientation of mass on plane. • Direction of Normal Force. • Confusing sin and cos. 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Administrative Issues • EXAM 1: Monday, IN CLASS! – Equation sheet given • If you rely on this, you will run out of time!! – – – – Wait outside class Practice Exams Pens/Pencils and Calculators are all that are allowed! No iPods/mp3 players • Exam Review session – Thursday evening, OH218, 6:30 pm. – Come with questions!! I will work out whatever you ask, but session ends when you run out of questions. 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Outline • • Friction Velocity dependent Forces • What do we know? – – – – – – – – – – – – Units Kinematic equations Freely falling objects Vectors Kinematics + Vectors = Vector Kinematics Relative motion Projectile motion Uniform circular motion Newton’s Laws Force of Gravity and Normal Force Free Body Diagrams Problem Solving 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Review Problem 50m 250m 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Solve for acceleration, velocity • Geometry • Free-body diagram • Forces 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Zip-Line problem • a, vf 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Up to now… • We have worked with frictionless surfaces and no air resistance. • Not particularly realistic! • If I apply a Force to an object on this table, does it keep moving forever? 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Friction • Friction is actually a microscopic effect. – The roughness of two surfaces sliding against one another provides a Force opposite to the direction of motion. – The magnitude of this force depends on two things: • The properties of the two surfaces • The Normal Force between the two surfaces. 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Coefficient of Kinetic Friction • Sliding Friction • Force acting against sliding motion of object on a surface F fr k FN k Coefficient of kinetic friction Depends on surfaces Magnitude of Ffr depends on FN, but direction is ALWAYS against direction of motion. Not a fundamental law Experimental Result 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Friction Example • Suppose we consider the 3 examples from last lecture. Let’s rank the Frictional Forces for a mass sliding on a surface with coefficient of static friction k A C B -FH FFR vo FFR 95.141, F2010, Lecture 8 Department of Physics and Applied Physics +FH vo FFR vo In Class Demo • Pull on book from rest – What is Force required to start book moving? – What is Force required to keep book moving once it has started? – What happens to the magnitude of this Force if I press down on the book? 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Two Types of Friction • Kinetic Friction: associated with movement • Static Friction: Friction at rest – If I push on an object on the ground and it doesn’t move, I am exerting a Force, and since the object isn’t moving, there must be a second Force opposing my Force. This Force is the Force of Static Friction • The expression for Static Friction is slightly different than for Kinetic Friction. • Still depends on FN FSfr s FN 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Static Friction • Imagine a 10.2kg box on the ground, at rest. The system has a coefficients friction μs=0.5, and μk=0.3. • I push (horizontally) with a Force 20N. What is acceleration? • I push a little harder (F=40N)…Does it move? • I push with a Force of 60N. What is acceleration now? 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Static Friction • Imagine a 10.2kg box on the ground, at rest. The system has a coefficients friction μs=0.5, and μk=0.3. • I push (horizontally) with a Force 50N. Does it move? What is acceleration? • I push with a Force of 60N. What is acceleration now? 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Demo: Static Friction • Case 1: only a couple of pages overlap • 10 pages overlap • Every other page 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Example I (Kinetic and Static Friction) • A block lies on an inclined plane (μk=0.3, μs=0.5). At what angle do you see the block start to move? What is the acceleration when θ=45º? • Choose coordinate system • Draw Free Body Diagram 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Example I (Kinetic and Static Friction) • A block lies on an inclined plane (μk=0.3, μs=0.5). At what angle do you see the block start to move? • Write out Force components F F mg cos 0 Fx mg sin Ffr mg sin s FN y N mg sin s mg cos max 27 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Die Hard with a Physics Vengeance 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Die Hard with a Physics Vengeance 40º S 1.0 k 0.8 What is acceleration with a) wheels spinning? b) wheels locked? 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Die Hard with a Physics Vengeance k 0.8 40º 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Die Hard with a Physics Vengeance s 1.0 40º 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Velocity-Dependent Forces • Friction is relatively easy, it just has two values, depending on whether the object is moving or at rest. • Friction does not depend on the velocity of the object! • Some forces, however, do depend on the velocity of the object. 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Drag Forces • Force acting on an object as it moves through a Fluid or Gas. – Boat in water – Any motion in air • Cars • Skydivers • Projectile motion • Mathematics of velocity dependent Forces is tricky, but a good approximations are: FD bv 2 FD bv 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Terminal Velocity • If we assume drag force is: FD bv • What is terminal velocity of a skydiver? 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Terminal Velocity II 2 F bv • If we assume drag force is: D • What is terminal velocity of a skydiver? 95.141, F2010, Lecture 8 Department of Physics and Applied Physics Now we Know • Force problems with friction – – – – Draw diagram Draw free body diagram Divide Forces into components Obtain equations of motion for each dimension • Velocity Dependent Forces – Terminal Velocity 95.141, F2010, Lecture 8 Department of Physics and Applied Physics