1. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Chapter 4

2. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Goals for Chapter 4 To understand force – either directly or as the net force of multiple components. To study and apply Newton’s First Law. To study and apply the concept of mass and acceleration as components of Newton’s Second Law. To differentiate between mass and weight. To study and apply Newton’s Third Law. To open a new presentation of problem data in a free body diagram.

3. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Dynamics, a new frontier Stated previously, the onset of physics separates into two distinct parts: – statics and – dynamics. So, if something is going to be dynamic, what causes it to be so? – A force is the cause, it is either pushing or pulling.

4. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Types of Force Illustrated I – Figure 4.1

5. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Types of Force II – Figure 4.2 Single or net – Contact force – Normal force – Frictional force – Tension – Weight

6. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley A force may be resolved into components – Figure 4.4 F x = F CosΘ F y = F SinΘ

7. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Components and Resultants II – Figure 4.6 An example of component resolution.

8. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

11. R = F 1 + F 2 + F 3 + ……..= Σ F, (resultant, and vector sum, of forces) R x = Σ F x, R y = Σ F y (components of vector sum of forces) Once we have the components R x and R y, we can find the magnitude and direction of the vector R.

12. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley HOMEWORK 3; 5; 12; 13; 17; 18; 20; 22; 26; 28; 30; 31; 33; 35; 36; 37; 38

13. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Newton’s First Law – Figure 4.7 “Objects at rest tend to stay at rest and objects in motion tend to stay in motion in a straight line unless it is forced to change that state by forces acting on it”

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15. R = F 1 + F 2 = 0 Zero resultant force is equal to no force at all. When an object is acted on by no forces or by several forces whose vector sum (resultant) is zero, we say that the object is in equilibrium, R = Σ F = 0 (equilibrium under zero resultant force) Each component of R must be zero, so Σ F x = 0, Σ F y = 0. (object in equilibrium)

16. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley We determine effect with the net force. – Figure 4.8

17. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

21. Mass and Newton’s Second Law II – Figure 4.12 Let’s examine some situations with more than one mass.

22. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley INERTIA

23. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Newton’s Second Law of Motion (Vector Form) The vector sum (resultant) of all the forces acting on an object equals the object’s mass times its acceleration : ΣF = ma The acceleration a has the same direction as the resultant force ΣF.

24. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Newton’s Second Law of Motion (Components Form) For an object moving in a plane, each component of the total force equals the mass times the corresponding component of acceleration: ΣF x = ma x ΣF x = ma x

25. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Definition of the newton One newton is the amount of force that gives an acceleration of 1 meter per second squared to an object with a mass of 1 kilogram. That is, 1 N = (1 kg) ( 1 m/s 2 )

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28. ON THE MOON

29. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Measurement of mass – Figure 4.20 Since gravity is constant, we can compare forces to measure unknown masses.

30. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Forces are the origin of motion Forces Acceleration a=F/m Velocity v= v 0 + at Position x = x 0 + v 0 t + ½ at 2

31. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Forces and free body diagrams we account for the forces and draw a free body diagram. In this case, the net force is unbalanced. This is a good example of forces in dynamics.

32. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Newton’s Third Law

33. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Newton’s Third Law “For every action there is an equal and opposite reaction.” Rifle recoil is a wonderful example.

34. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley For two interacting objects A and B, the formal statement of Newton’s third law is F A on B = -F B on A Newton’s own statement, translated from the latin of the Principia, is To every action there is always opposed an equal reaction; or, the mutual actions of two objects upon each other are always equal, and directed to contrary parts. Newton’s Third Law

35. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Free-Body Diagram

36. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

37. Use free body diagrams in any situation – Figure 4.24 Find the object of the focus of your study and collect all forces acting upon it

38. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley Homework 3, 9, 14, 20, 21, 23, 30, 34, 41, 52