1. University Physics: Mechanics Ch6. Friction, Drag, and Centripetal Force Lecture 9 Dr.-Ing. Erwin Sitompul http://zitompul.wordpress.com 2013

2. 9/2 Erwin SitompulUniversity Physics: Mechanics A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support, as in the figure below. The upper cables make angles of 37° and 53° with the horizontal. These upper cables are not as strong as the vertical cable and will break if the tension in them exceeds 100N. Will the traffic light remain hanging in this situation, or will one of the cables break? Homework 7: The Traffic Light

3. 9/3 Erwin SitompulUniversity Physics: Mechanics Free-Body Diagram for the Traffic Light Free-Body Diagram for the Knot Solution of Homework 7: The Traffic Light

4. 9/4 Erwin SitompulUniversity Physics: Mechanics Both values of T 1 and T 2 are less than 100 N. So, the cables will not break. Why zero? Forces along the x axis: Forces along the y axis: Why zero? Solution of Homework 7: The Traffic Light

5. 9/5 Erwin SitompulUniversity Physics: Mechanics Friction  Frictional forces are unavoidable in our daily lives.  If we were not able to counteract them, they would stop every moving object and bring every rotating shaft to a halt. About 20% of the gasoline used in a car is needed to counteract friction.  On the other hand, if friction were totally absent, we could not get an automobile to go anywhere, and we could not walk or ride a bicycle. Nobody can hold a pencil and it would not write.  Here we deal with the frictional forces that exist between dry solid surfaces, either stationary relative to each other (static) or moving across each other at slow speeds (kinetic).  The friction is a passive force. When a force is applied to an object, the friction force arises against it. f s : static frictional force f k : kinetic frictional force → →

6. 9/6 Erwin SitompulUniversity Physics: Mechanics Friction No motion A block rests on a tabletop with the gravitational force balanced by a normal force. There is no friction force, An increasing force is applied to the block, attempting to pull it to the left. The block does not move. An equal and opposite static frictional force arises between the object and the surface, exactly balancing the applied force. (a)(a) (b)(b)(c)(c)(d)(d)

7. 9/7 Erwin SitompulUniversity Physics: Mechanics Friction Acceleration Constant velocity (e)(e) (f)(f) Eventually the object will be accelerated when the applied force reaches a certain magnitude. The frictional force that oppose the motion is now the kinetic frictional force, The magnitude of the kinetic frictional force, which acts when there is motion, is less than the maximum magnitude of the static frictional force, which acts when there is no motion. To move the block across the surface with a constant speed, the magnitude of the applied force must be decreased once the block begins to move,

8. 9/8 Erwin SitompulUniversity Physics: Mechanics (a)(a)(b)(b)(c)(c)(d)(d)(e)(e)(f)(f) Friction

9. 9/9 Erwin SitompulUniversity Physics: Mechanics Two surfaces In Contact  When two ordinary surfaces are placed together, only the high points touch each other.  Some contact points do cold-welt together. These welds produce static friction when an applied force attempts to slide the surface relative to each other.  If the applied force is great enough to pull one surface across the other, there is first a tearing of welds (at breakaway) and then a continuous re-forming and tearing of welds as movement occurs.  If the two surfaces are pressed together harder, many more points cold-weld. Sliding the surfaces relative to each other requires a greater applied force. Friction

10. 9/10 Erwin SitompulUniversity Physics: Mechanics  Experiment shows that when a body presses against a surface and a force F attempts to slide the body along the surface, the resulting frictional force has three properties.  Property 1 If the body does not move, then the static frictional force f s and the component of F that is parallel to the surface balance each other. They are equal in magnitude, and oppose in direction.  Property 2 The magnitude of f s has a maximum value f s,max that is given by  Property 3 If he body begins to slide along the surface, the magnitude of the frictional force rapidly decreases to a value f k given by → → → → μ s : coefficient of static friction μ k : coefficient of kinetic friction Properties of Friction

11. 9/11 Erwin SitompulUniversity Physics: Mechanics  Friction depends on how strongly the surfaces are pressed together. This pressing strength is represented by the normal force F N.  It is easier to keep an object sliding than to get it starts sliding. →  The coefficients μ s and μ k are dimensionless and must be determined experimentally.  The value of μ s and μ k depends on certain properties of both the body and the surface. Therefore, they are usually referred to with the preposition “between.” Properties of Friction

12. 9/12 Erwin SitompulUniversity Physics: Mechanics A block lies on a floor. (a)What is the magnitude of the frictional force on it from the floor? (b)If a horizontal force of 5 N is now applied to the block, but the block does not move, what is the magnitude of the frictional force on it? (c)If the maximum value of f s,max of the static fictional force on the block is 10 N, will the block move if the magnitude of the horizontally applied force is 8 N? (d)What about if it is 12 N? (e)What is the magnitude of the frictional force in part (c)? Zero 5 N No Yes 8 N Properties of Friction

13. 9/13 Erwin SitompulUniversity Physics: Mechanics If a car’s wheels are “locked” (kept from rolling) during emergency braking, the car slides along the road. Ripped-off bits of tire and small melted sections of road form the “skid marks.” The record for the longest skid marks on a public road was reportedly set in 1960 by a Jaguar on the M1 highway in England – the marks were 290 m long. Assuming that μ k = 0.6 and the car’s acceleration was constant during the braking, how fast was the car going when the wheels became locked? Example: Jaguar

14. 9/14 Erwin SitompulUniversity Physics: Mechanics Example: Jaguar

15. 9/15 Erwin SitompulUniversity Physics: Mechanics F 1 = 10 N is applied to a box on a floor, but the box does not slide. Then, F 2 is increased from zero. Before the box begins to slide, do the following quantities increase, decrease, or stay the same? (a)The magnitude of the frictional force on the box. (b)The magnitude of the normal force on the box from the floor. (c)The maximum value f s,max of the static frictional force on the box. → → The same, 10 N Decrease Decrease Checkpoint

16. 9/16 Erwin SitompulUniversity Physics: Mechanics A 2.5 kg block is initially at rest on a horizontal surface. A horizontal force F of magnitude 6 N and a vertical force P are then applied to the block (see below). The coefficients of friction for the block and surface are μ s = 0.4 and μ k = 0.25. Determine the magnitude of the frictional force acting on the block if the magnitude of P is (a) 8 N (b) 10 N (c) 12 N →→ → Example: Amber Block

17. 9/17 Erwin SitompulUniversity Physics: Mechanics FNFN → FgFg → f → On the verge of sliding, the maximum static frictional force is: Forces along the y axis: The box does not move The box moves Example: Amber Block

18. 9/18 Erwin SitompulUniversity Physics: Mechanics The figure below shows a coin of mass m at rest on a book that has been tilted at an angle θ with the horizontal. By experimenting, you find that when θ is increased to 13°, the coin is on the verge of sliding down the book, which means that even a slight increase beyond 13° produces sliding. What is the coefficient of static friction μ s between the coin and the book? Hint: Draw the free-body diagram of the coin first. Homework 8: Coin On A Book

19. 9/19 Erwin SitompulUniversity Physics: Mechanics Homework 8A A car accident happened in which car A slid into the rear of car B, which was stopped at a red light along a road headed down a hill (see figure). The slope of the hill is θ  12° and the cars were separated by distance d  24 m when the driver of car A put the car into a slide, while the speed of car A at the onset of braking was v 0  18 m/s. With what speed did car A hit car B if the coefficient of kinetic friction was (a) 0.6 (dry road surface) and (b) 0.10 (road surface covered with wet leaves)?

20. 9/20 Erwin SitompulUniversity Physics: Mechanics Homework 8B 1.A woman pulls a loaded sled, with a mass of 75 kg, along a horizontal surface at a constant speed. She is pulling with a rope at an angle of 42° with the horizontal and the coefficient of friction between the runners and the snow is 0.1. (a) What is the tension in the rope? (b) If the woman increases her pull on the rope, so that T is greater than 91 N, is the magnitude of f k greater than, less than, or the same as in (a)? 2.Two post boxes at FedEx start sliding down the 20° ramp shown in the next figure. Box A has a mass of 5.0 kg and a coefficient of friction of 0.20. Box B has a mass of 10 kg and a coefficient of friction of 0.15. How long does it take box A to reach the bottom? Answer: 1.48 s.