1. © 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. Lecture Powerpoints Physics for Scientists and Engineers, 3 rd edition Fishbane Gasiorowicz Thornton

2. Chapter 5 Applications of Newton’s Laws

3. Main points of Chapter 5 Gravity, tension, normal force revisited Friction, static and kinetic Drag forces Circular motion Fundamental forces

4. 5-1 Common Forces Revisited Gravity The acceleration is the gravitational force divided by the inertial mass: The force is the acceleration of gravity multiplied by the gravitational mass: Therefore, the inertial and gravitational masses are equal: (5-1) (5-2) (5-3)

5. 5-1 Common Forces Revisited Tension Tension always pulls, never pushes. For light (negligible-mass) ropes, the magnitude of the tension is the same everywhere along the rope.

6. 5-1 Common Forces Revisited The Normal Force Normal force is always perpendicular to surface:

7. Applying Newton’s Laws with Constant Forces (5-8) (5-9) 5-1 Common Forces Revisited If force is constant, acceleration is constant: These equations apply to each component.

8. 5-2 Friction Static and kinetic friction Static friction applies when object is not moving along surface; kinetic applies when it is moving Both types of friction depend on the normal force

9. 5-2 Friction Static and kinetic friction The friction force is always opposite to the direction of motion (or the direction motion would occur, in the case of static friction)

10. 5-2 Friction Static frictional force starts at zero (if no opposing horizontal force components) and increases linearly with the force up to its maximum value.

11. 5-2 Friction Kinetic frictional force is somewhat smaller than static, so that when object begins to move it accelerates if force stays constant. Otherwise can lessen force to maintain constant speed. In either case, force of kinetic friction does not depend on speed.

12. 5-2 Friction Forces when pushing box from dead start:

13. Static friction: Kinetic friction: Here, μ is the coefficient of friction, and F N is the normal force. (5-21) (5-22) 5-2 Friction

14. 5-3 Drag Forces Drag forces come from fluids – gas or liquid – and are generally proportional to the square of the speed of the object So, as falling object accelerates, drag force gets bigger and bigger, until it is equal to accelerating force At this point, the net force on the object is zero, and it moves at a constant velocity from then on; this is called the terminal velocity

15. 5-3 Drag Forces Here, F D is the drag force; ρ the density of the medium; A the cross-sectional area of the object; C D the drag coefficient. (5-30)

16. 5-4 Forces and Circular Motion (5-34) We already know that objects in circular motion move with a centripetal acceleration: (5-33) Therefore, there must be a centripetal force:

17. 5-4 Forces and Circular Motion In this diagram, the centripetal force is supplied by the rope:

18. 5-4 Forces and Circular Motion Circular Motion with Changing Speed If speed is changing, there must be a component of the force parallel to the velocity; this means that the acceleration has both tangential and radial components.

19. 5-4 Forces and Circular Motion Circular Motion with Changing Speed Look at a pendulum: The gravitational force on it points straight down, and therefore has a tangential component.

20. Radial component of acceleration: Tangential component: 5-4 Forces and Circular Motion Circular Motion with Changing Speed Force diagram: Components of gravitational force:

21. Circular Motion and Noninertial Frames 5-4 Forces and Circular Motion In this example, centripetal force is provided by normal force Astronaut is in noninertial reference frame Centrifugal force that she feels is not a true force

22. 5-5 Fundamental Forces Universal gravitation: gravitational force between any two masses Electroweak force: includes electric, magnetic, and weak nuclear forces (responsible for radioactive decay) Strong (nuclear) force: binds protons and neutrons together in nucleus All will be discussed at greater length in subsequent chapters.

23. Summary of Chapter 5 Force of gravity: Tension: always a pulling force; if rope’s mass is negligible, tension is constant throughout Normal force: perpendicular to surface; equal to force towards surface Static friction is variable, depending on applied force: Kinetic friction is constant: Frictional force always opposes direction of motion (5-2) (5-21) (5-22)

24. Summary of Chapter 5, cont. Drag force arises when object travels through fluid: In uniform circular motion, the force is centripetal: (5-30) (5-34) Fundamental forces: gravitation, electroweak, strong nuclear