1. Copyright © 2010 Pearson Education, Inc. Lecture Outline Chapter 6 Physics, 4 th Edition James S. Walker

2. Copyright © 2010 Pearson Education, Inc. Chapter 6 Applications of Newton’s Laws

3. Copyright © 2010 Pearson Education, Inc. Units of Chapter 6 Frictional Forces Strings and Springs Translational Equilibrium Connected Objects Circular Motion

4. Copyright © 2010 Pearson Education, Inc. 6-1 Frictional Forces Friction has its basis in surfaces that are not completely smooth:

5. Copyright © 2010 Pearson Education, Inc. 6-1 Frictional Forces Kinetic friction: the friction experienced by surfaces sliding against one another The static frictional force depends on the normal force: (6-1) The constant is called the coefficient of kinetic friction.

6. Copyright © 2010 Pearson Education, Inc. 6-1 Frictional Forces

7. Copyright © 2010 Pearson Education, Inc. 6-1 Frictional Forces The kinetic frictional force is also independent of the relative speed of the surfaces, and of their area of contact.

8. Copyright © 2010 Pearson Education, Inc. The static frictional force keeps an object from starting to move when a force is applied. The static frictional force has a maximum value, but may take on any value from zero to the maximum, 6-1 Frictional Forces depending on what is needed to keep the sum of forces zero.

9. Copyright © 2010 Pearson Education, Inc. 6-1 Frictional Forces (6-2) where (6-3) The static frictional force is also independent of the area of contact and the relative speed of the surfaces.

10. Copyright © 2010 Pearson Education, Inc. 6-2 Strings and Springs When you pull on a string or rope, it becomes taut. We say that there is tension in the string.

11. Copyright © 2010 Pearson Education, Inc. 6-2 Strings and Springs The tension in a real rope will vary along its length, due to the weight of the rope. Here, we will assume that all ropes, strings, wires, etc. are massless unless otherwise stated.

12. Copyright © 2010 Pearson Education, Inc. 6-2 Strings and Springs An ideal pulley is one that simply changes the direction of the tension:

13. Copyright © 2010 Pearson Education, Inc. 6-2 Strings and Springs Hooke’s law for springs states that the force increases with the amount the spring is stretched or compressed: The constant k is called the spring constant.

14. Copyright © 2010 Pearson Education, Inc. 6-3 Translational Equilibrium When an object is in translational equilibrium, the net force on it is zero: (6-5) This allows the calculation of unknown forces.

15. Copyright © 2010 Pearson Education, Inc. 6-3 Translational Equilibrium

16. Copyright © 2010 Pearson Education, Inc. 6-4 Connected Objects When forces are exerted on connected objects, their accelerations are the same. If there are two objects connected by a string, and we know the force and the masses, we can find the acceleration and the tension:

17. Copyright © 2010 Pearson Education, Inc. 6-4 Connected Objects We treat each box as a separate system:

18. Copyright © 2010 Pearson Education, Inc. 6-4 Connected Objects If there is a pulley, it is easiest to have the coordinate system follow the string:

19. Copyright © 2010 Pearson Education, Inc. 6-5 Circular Motion An object moving in a circle must have a force acting on it; otherwise it would move in a straight line. The direction of the force is towards the center of the circle.

20. Copyright © 2010 Pearson Education, Inc. 6-5 Circular Motion Some algebra gives us the magnitude of the acceleration, and therefore the force, required to keep an object of mass m moving in a circle of radius r. The magnitude of the force is given by: (6-15)

21. Copyright © 2010 Pearson Education, Inc. 6-5 Circular Motion This force may be provided by the tension in a string, the normal force, or friction, among others.

22. Copyright © 2010 Pearson Education, Inc. 6-5 Circular Motion

23. Copyright © 2010 Pearson Education, Inc. 6-5 Circular Motion An object may be changing its speed as it moves in a circle; in that case, there is a tangential acceleration as well:

24. Copyright © 2010 Pearson Education, Inc. Summary of Chapter 6 Friction is due to microscopic roughness. Kinetic friction: Static friction: Tension: the force transmitted through a string. Force exerted by an ideal spring:

25. Copyright © 2010 Pearson Education, Inc. Summary of Chapter 6 An object is in translational equilibrium if the net force acting on it is zero. Connected objects have the same acceleration. The force required to move an object of mass m in a circle of radius r is: