1. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Physics I 95.141 LECTURE 8 9/29/10

2. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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?

3. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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).

4. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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?

5. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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?

6. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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?

7. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Common Mistakes Orientation of mass on plane. Direction of Normal Force. Confusing sin and cos.

8. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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.

9. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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

10. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Review Problem 50m 250m

11. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Solve for acceleration, velocity Geometry Free-body diagram Forces

12. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Zip-Line problem a, v f

13. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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?

14. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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.

15. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Coefficient of Kinetic Friction Sliding Friction Force acting against sliding motion of object on a surface Coefficient of kinetic friction Depends on surfaces Magnitude of F fr depends on F N, but direction is ALWAYS against direction of motion. Not a fundamental law  Experimental Result

16. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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 -F H +F H F FR A B C

17. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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?

18. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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 F N

19. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Static Friction I push a little harder (F=40N)…Does it move? Imagine a 10.2kg box on the ground, at rest. The system has a coefficients friction μ s =0.5, and μ k =0.3. I push (horizontally) with a Force 20N. What is acceleration? I push with a Force of 60N. What is acceleration now?

20. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Static Friction Imagine a 10.2kg box on the ground, at rest. The system has a coefficients friction μ s =0.5, and μ k =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?

21. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Demo: Static Friction Case 1: only a couple of pages overlap 10 pages overlap Every other page

22. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Example I (Kinetic and Static Friction) A block lies on an inclined plane (μ k =0.3, μ s =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

23. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Example I (Kinetic and Static Friction) A block lies on an inclined plane (μ k =0.3, μ s =0.5). At what angle do you see the block start to move? Write out Force components

24. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Die Hard with a Physics Vengeance

25. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Die Hard with a Physics Vengeance 40º What is acceleration with a)wheels spinning? b)wheels locked?

26. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Die Hard with a Physics Vengeance 40º

27. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Die Hard with a Physics Vengeance 40º

28. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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.

29. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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:

30. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Terminal Velocity If we assume drag force is: What is terminal velocity of a skydiver?

31. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 Terminal Velocity II If we assume drag force is: What is terminal velocity of a skydiver?

32. Department of Physics and Applied Physics 95.141, F2010, Lecture 8 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