1. Unit 6: Applications of Newton’s Laws

2. Sections A and B: Friction Corresponding Book Sections: –6.1 PA Assessment Anchors: –S11.C.3.1

3. What’s different now? In the last unit, we didn’t account for a very important force: –Friction The resistance exerted on an object while it’s in motion

4. Kinetic Friction The friction encountered when surfaces slide against each other with some speed Symbol: f k

5. So, how does friction affect different objects? The object with twice the mass has twice the friction acting on it. But why…?

6. Kinetic Friction, derived… Kinetic friction is proportional to the Normal Force. f k = µ k N Force of kinetic friction = Coefficient of kinetic friction x Normal force (Pronounced “Mew”)

7. Coefficient of Kinetic Friction As this increases, so does the force of friction between two objects.

8. Basic facts about Kinetic Friction 1. Proportional to the Normal Force f k = µ k N 2. Does not depend on speed of the objects 3. Does not depend on area of contact between the surfaces

9. Practice Problem #1 Refer to Example 6-1

10. FBD for Example 6-1

11. Static Friction The friction that tends to keep two objects from moving relative to each other This is usually stronger than kinetic friction because surfaces can form a stronger connection

12. Static Friction, cont… f s, max = µ s N The maximum static frictional force will occur immediately before the object starts moving. This is when kinetic friction will take over. Maximum static force of friction = Coefficient of static friction x Normal force

13. Changing from Static to Kinetic No Applied Force Small Applied Force Big Applied Force Largest Applied Force Kinetic Friction Takes Over

14. Basic facts about Static Friction 1. Can be any value between 0 and f s, max = µ s N 2. Does not depend on area of contact between the surfaces 3. Is parallel to contact surface and in direction opposite that of motion

15. Practice Problem #1 Refer to Example 6-3, Page 143

16. FBD For Practice Problem #1

17. Is the friction between a car’s tires and the roads kinetic and static? Think about how you walk With each step, your foot is in contact with the ground (static friction) This is what your car is doing really really quickly

18. A picture to help explain…

19. Skidding vs. Braking Why are anti-lock brakes desirable? –When a car skids, the friction acting on it is kinetic –When a car brakes (wheels still rolling), the friction acting on it is static

20. A picture to explain…

21. Section C: Tension Corresponding Book Sections: –6.2, 6.3, 6.4 PA Assessment Anchors: –S11.C.3.1

22. Tension The force on a string that would be required to hold the string together if it was cut at any point

23. Practice Problem #1 What is the tension force required to hold a 50 kg object motionless above the ground?

24. Practice Problem #2 How much tension force is needed to pull a 10 kg object with an acceleration of 3.5 m/s 2 if the coefficient of kinetic friction is 0.4?

25. Practice Problem #3 Refer to Example 6-4, Page 147

26. FBD for Example 6-4

27. Section D: Springs Corresponding Book Sections: –6.2 PA Assessment Anchors: –S11.C.3.1

28. Hooke’s Law A spring stretched or compressed by the amount x from its equilibrium exerts a force given by: F = - kx k = force constant or spring constant –Units: N/m

29. Generally Speaking… If a spring is compressed:  F = -kx This makes “x” negative If a spring is stretched:  F = kx This makes “x” positive

30. Practice Problem #1 A 1.5 kg object hangs motionless from a spring with force constant of k = 250 N/m. How far is the spring stretched?

31. Practice Problem #2 What amount of spring force is needed to pull a 40 kg object with constant speed if the coefficient of kinetic friction is 0.25?

32. Section E: Centripetal Motion Corresponding Book Sections: –6.5 PA Assessment Anchors: –S11.C.3.1

33. What is centripetal motion? Centripetal Acceleration –A “center directed” acceleration Motion where the direction of the velocity changes continuously

34. How do we find centripetal acceleration? Direction is towards center of circle Equation:

35. How do we find the centripetal force? Directed toward center of circle

36. Practice Problem #1 Refer to Example 6-8 on page 159

37. Practice Problem #2 Refer to Example 6-9 on page 161