1. Frictional Forces

2. Question: how does a highway patrol officer use skid marks to recreate an accident?

3. What produces skid marks on the road? The wheels on a car lock, and rub the surface of the road As this occurs, the car slows down Why? Frictional forces

4. Friction: The Force that Slows Us http://phet.colorado.edu/new/simulations/si ms.php?sim=Frictionhttp://phet.colorado.edu/new/simulations/si ms.php?sim=Friction On what does this force depend? How do we quantify it?

5. The frictional coefficient describes the interaction between two surfaces Symbol is  The higher the value, the rougher the surface interaction

6. Which surface interaction would have the highest frictional coefficient? 1.Ice rubbing against ice 2.Wood on a table top 3.Wood on mouse pad 4.Water on rock 5.Teflon on glass

7. Consider three surface interactions: Rubber on glass (A), rubber on concrete (B), and rubber on ice (C). Rank these in order of decreasing . 1.A, B, C 2. B, A, C 3.A, C, B 4.C, A, B 5. B, C, A

8. Some Values

9. Other Factors? Quick Experiment: Slide your textbook across the desk Now slide it across the desk while you push down upon it Which produces more friction Why? We’re increasing the normal force

10. Frictional Calculations Friction Force =  N This works for both static and kinetic friction

11. A 1000kg car screeches to a halt on a surface with  = 0.5. Calculate the frictional force acting upon the car

12. Think about pencil sitting at rest on the top of your text book. As you tilt the cover of your book, what happens to the frictional force? 1.It increases 2.It decreases 3.It stays the same 4.Who cares, the NCAA tournament is 7 weeks away Think about why you chose your answer

13. Imagine a highway patrol officer, arriving at the scene of an accident He uses something called a drag sled to determine the amount of friction produced by the road

14. Assuming he applies a 40N force to pull a 5kg drag sled at constant velocity across a horizontal road way, what is the coefficient of friction between the road way and drag sled?

15. So if he knows  for the interaction between roads and tires, how will he figure out the car’s acceleration? Newton’s 2 nd law! Frictional Force =  N = ma

16. Another car, mass 2000kg slides across a slick road with  = 0.2. Calculate the magnitude of this car’s acceleration Bonus Question: How would this acceleration compare to that of a 4000kg car?

17. A 3900kg Hummer has an acceleration of 5.9m/s 2 as it slides to a stop. What was the coefficient of friction between the Hummer’s tires and the road way?

18. Friction Types Static friction is the force of friction that keeps an object at rest Kinetic friction acts on the object once it is moving Which is larger?

19. Some Values

20. The 3900kg Hummer, moving at 20m/s, locks its brakes and starts skidding on a road with frictional coefficient 0.75. What minimum distance does the Hummer need to stop?

21. Friction in Multiple Dimensions A traveler pulls his rolling bag at constant velocity across a horizontal surface by applying a 50N force, directed at an angle of 45 above the horizontal. Assuming the bag’s mass is 10kg: Find the normal force acting on the bag Find the frictional force acting on the bag Find the coefficient of friction between the ground and bag

22. If the traveler from the previous problem pulls his bag with a force of 30N, directed at 30 above the horizontal, find the bag’s acceleration across the floor

23. Inclined Planes and Friction The ancient Egyptians used inclined planes to help build the pyramids How did they ensure that the blocks they were pulling didn’t slide back down the ramp and kill them?

24. Think about a book (m = 1.5kg), lying at rest on a slanted table (makes an angle of 15 with the horizontal) Draw a force diagram for this book Find the frictional force acting on the book Find the normal force, and the coefficient of friction between table and book

25. Hitting the Slopes… A snowboarder (m = 95kg) travels down a hill at an angle of 25 above the horizontal Assuming the skier travels at constant velocity, find the frictional force acting on the skier, and  k

26. Force = 400N Coefficient = 0.47

27. Now we all know that snowboarders speed up as they go down a slope Assuming the same mountain from before, with  = 0.2, find the snowboarder’s acceleration Given such a low friction coefficient, how does the skier slow down (ie, which forces slow her down)?

28. a = 2.4 m/s/s

29. Building the Pyramids Constructed from approximately 2580- 2560 BCE The world’s tallest structure (480 ft, now 460ft) for over 3000 years The pyramid contains 2 million blocks, each weighing 1.5 tons Some materials were transported over 500 miles to the construction site A truly massive undertaking (no pun intended…)

30. http://maps.google.com/

31. Moving a Block up a Ramp Let’s think about moving one block (W = 1.5 tons = 20,000N) up a ramp of unknown angle Assuming the coefficient of static friction between the ramp and block is 0.6, find the maximum angle of inclination at which the block will remain at rest

32. Theta = 31 degrees above the horizontal

33. Now, assuming the coefficient of kinetic friction between the block and ramp is 0.5, find the minimum force necessary to pull the block up a ramp at an inclination of 15 degrees

34. If the block gets pulled with a force of 20kN up the ramp, what is the block’s acceleration?

35. Using Pulleys to Help Imagine using a pulley system to aid in your block lifting (although the Egyptians had not yet thought of pulley-systems)

36. In the absence of friction, find the acceleration of block 1

37. Assuming a kinetic frictional coefficient of 0.4, calculate the mass of the hanging block necessary to make the second block slide up the ramp at constant velocity