1. Friction M1 A-level Mechanics © Adam Gibson

2. Friction What are the properties of a frictional force? When the object is moving, friction acts in the opposite direction to motion When the object is stationary, friction opposes the direction in which motion would occur How can we know the magnitude of the frictional force? If the object is at rest (STATICS), the frictional force is just big enough to prevent motion The frictional force has a MAXIMUM or “limiting” value:

3. Limiting friction Now we start to tilt the slope Suppose the box is stationary Does the box move? Eventually, it slips. But at what angle θ does it slip? Does it depend on the weight? Does it depend on anything else? θ Remember: box slope

4. Limiting friction - 2. Let’s draw the forces carefully. = weight =W = normal contact =N = friction =f Note – these are the forces acting on the BOX, not the slope. θ

5. Limiting friction - 3. θ θ W Given the relationship, write two general equations for this situation. The friction force f will reach its maximum value just at the time when the box slips.

6. Limiting friction - 3. θ θ W Resolving parallel to the plane: Resolving perpendicular to the plane: “angle of friction”

7. Limiting Friction 4 Exercise – Suppose μ = 1.0, and that the weight of the box is 8N. Sketch a graph showing the relationship between frictional force f and angle θ between the slope and the horizontal. Answer: 45° Box starts to slip

8. Limiting friction - 5. A note about words. “Just about to slip” “Just about to move” “On the point of moving” “Frictional force has its limiting value” “In limiting equilibrium” - is called the “coefficient of friction”. It is not necessarily < 1, but usually is. It depends mainly on the materials (e.g. wood, glass etc.) (NB static vs. dynamic – we ignore) What are the units of ? No units – a number. all mean the same thing.

9. THE LAWS OF FRICTION. When the surfaces of two objects are in rough contact, and have a tendency to move relative to one another, equal and opposite frictional forces act, one on each of the objects, so as to oppose the potential movement. Until it reaches its limiting value, the magnitude of the frictional force is just sufficient to prevent motion. When the limiting value is reached,, where μ is the coefficient of friction for those two surfaces. For all rough contacts, If a contact is smooth,.

10. Book Work. Try the following exercises from your textbook: p. 66 Exercise 5A Questions 1,2,3,6,8,12 p. 74 Misc Ex 5 Questions 4,7,10 Homework is to be completed neatly and handed in before the end of Thursday. You will sit a short test on Statics in Week 4 (last lesson that week). The material in the test can be reviewed from p.43-46 (resolving forces), p. 60-66 (Friction) and from Chapter 10 (info. about resultants and equilibrium). Also from Powerpoint files which are available at sciemathsadam@gmail.com

11. THE REMAINING SLIDES ARE JUST A ROUGH WORKING AREA – IGNORE THEM

21. Saxon army Norman army Path of Norman horseman Path of Saxon horseman

31. backboard ball basket

35. Box 1 Box 2 15 m 5 m u ms -1

37. If these 5 forces act on one object, the object is in equilibrium, because they form a complete polygon

38. If one force is removed, the net force is of the same magnitude in the opposite direction

39. This is the displacement of P from 0 to T

41. arrives at Cleaves C arrives at B

42. required area is shaded Note: the sketch is not drawn “to scale” – but this is OK because it’s a sketch not a plot normal line

46. overhang