1. Aim: How do we explain the force of friction?

2. Visualizing Friction

3. Friction When an object is in contact with a surface, the surface exerts a contact force on the object. The contact force that acts parallel to the surface, opposing the motion of an object is called friction.

4. Static Friction vs Kinetic Friction Static friction- the force that must be overcome to set an object in motion. Static friction acts on objects at rest Kinetic Friction- the force of friction that acts on an object that is moving. Which is greater, the force of static friction or kinetic friction?

5. Equations for Friction F f static =< μ s F N F f kinetic = μ k F N F f = force of friction F N = normal force μ s = coefficient of static friction μ k = coefficient of kinetic friction

6. Sample Friction Problem 1.The coefficients of friction for an old physics book upon a shelf are: μ s = 0.50 and μ k = 0.40. Suppose the book has weight 14.5 N and a horizontal force is applied to it. (a) Determine the maximum force that can be applied without moving the book. (b) Determine the force required to keep the book moving at a constant speed across the shelf. (c) If the magnitude of the applied force is increased gradually, find the initial acceleration of the book just as it starts to move.

7. Thought Question 1 You press your physics textbook flat against a vertical wall with your hand. What is the direction of the friction force on the book exerted by the wall? a)Downwardc) Upward b)Outward from the walld) Into the wall

8. Sample Friction Problems 2. A car with speed v o applies the brakes and slows to a stop. Derive and simplify an equation for the stopping distance d in terms of v o and μ. (Use Newton’s equations of motion)

9. Thought Question 2 You are playing with your daughter in the snow. She is sitting on a sled and asking you to slide her across a flat, horizontal field. You have a choice of pushing from behind, by applying a force downward on her shoulders at 30 degrees below the horizontal, or attaching a rope to the front of the sled and pulling with a force at 30 degrees above the horizontal. Which would be easier for you and why?

10. Thought Question 2

11. Sample Friction Problem 3. A traveler pulls a suitcase of mass 8.00 kg across a level surface by pulling on the handle 20.0 N at an angle of 50.0° relative to horizontal. Friction against the suitcase can be modeled by μ k = 0.100. (a) Determine the acceleration of the suitcase. (b) What amount of force applied at the same angle would be needed to keep the suitcase moving at constant velocity?

12. Sample Friction Problems 4. A horse of mass 509 kg pulls a sleigh of mass 255 kg and both horse and sleigh accelerate at 0.500 m/s 2. The coefficient of friction for the sleigh is 0.15 as it moves over the snow. (a) Find the force that the horse must exert on the sleigh. (b) Determine the amount of horizontal force that the horse’s feet must exert.

13. Thought Question 3 A crate is located at the center of a flatbed truck. The truck accelerates toward the east, and the crate moves with it, not sliding on the bed of the truck. What is the direction of the friction force exerted by the bed of the truck on the crate? a)To the westc) To the east b)There is no friction force because the crate is not sliding

14. Problem 5 The driver of an empty speeding truck slams on the brakes and skids to a stop through a distance d. a)If the truck carries a heavy load such that its mass is doubled, what would be its skidding distance if it starts from the same initial speed? b)If the initial speed of the empty truck is halved, what would be the skidding distance?

15. Problem 5

16. Problem 6 The following is a simple method of measuring coefficients of friction. Suppose a block is placed on a rough surface inclined relative to the horizontal, as shown in the figure. The incline angle θ is increased until the block starts to move. a)How is the coefficient of static friction related to the critical angle θ c at which the block begins to move? b)How could we find the coefficient of kinetic friction?

17. Problem 6

18. Problem 7 A ball and a cube are connected by a light string that passes over a frictionless light pulley as shown. The coefficient of kinetic friction between the cube and the surface is 0.30. Find the acceleration of the two objects and tension in the string.

19. Problem 7

20. Problem 8 If the coefficient of kinetic friction were very large, the ball and cube could move with constant velocity. What coefficient is required for this situation to exist?

21. Problem 9 A warehouse worker places a crate on a sloped surface inclined at 30 degrees with respect to the horizontal. If the crate slides down the incline with an acceleration of magnitude g/3, determine the coefficient of kinetic friction between the crate and the surface.

22. Problem 9

23. Problem 10 A block moves up a 45 degree incline with constant speed under the action of a force of 15 N applied parallel to the incline. If the coefficient of kinetic friction is 0.300, determine (a)The weight of the block (b)The minimum force parallel to the incline required to allow it to move down the incline at constant speed.