Newton s Laws of Motion. Monday, September 26, 11

Transcription

1 Newton s Laws of Motion

2 Introduction We ve studied motion in one, two, and three dimensions but what causes motion? This causality was first studied in the late 1600s by Sir Isaac Newton. The laws are easy to state but intricate in their application. All around us we see Newton s laws in action. Easier than reading The Principia! Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

3 Introduction We ve studied motion in one, two, and three dimensions but what causes motion? This causality was first studied in the late 1600s by Sir Isaac Newton. The laws are easy to state but intricate in their application. All around us we see Newton s laws in action. Easier than reading The Principia! If I have seen further, it is by standing on the shoulders of giants. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

4 Force and Mass Force: push or pull Force is a vector it has magnitude and direction Copyright 2010 Pearson Education, Inc.

5 Force and Mass Mass is the measure of how hard it is to change an object s velocity. Mass can also be thought of as a measure of the quantity of matter in an object. Copyright 2010 Pearson Education, Inc.

6 What are the properties of force(s)? Combinations of push and pull Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

7 There are four common types of forces The normal force When an object rests or pushes on a surface, the surface pushes back. Frictional forces In addition to the normal force, surfaces can resist motion along the surface. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

8 There are four common types of forces Tension forces When a force is exerted through a rope or cable, the force is transmitted through that rope or cable as a tension. Weight Gravity s pull on an object. This force can act from large distances. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

9 How to denote a force Use a vector arrow to indicate magnitude and direction of the force. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

10 Use the net (overall) force Several forces acting on a point have the same effect as their vector sum acting on the same point. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

11 Decomposing a force into components F x and F y are the parallel and perpendicular components of a force to a sloping surface. Use F*Cosθ and F*Sinθ operations to find force components. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

12 Notation and method for the vector sum We refer to the vector sum or resultant as the sum of forces R = F 1 + F 2 + F 3 F n = ΣF. Use Tanθ = R y /R x and R = (R 2 x + R y2 ) 1/2. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

13 Superposition of forces Adding all x components and all y components allows you to add many vectors. This example has three. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

14 Newton s First Law of Motion Copyright 2010 Pearson Education, Inc.

15 Newton s First Law of Motion If you stop pushing an object, does it stop moving? Copyright 2010 Pearson Education, Inc.

16 Newton s First Law of Motion If you stop pushing an object, does it stop moving? Only if there is friction! Copyright 2010 Pearson Education, Inc.

17 Newton s First Law of Motion If you stop pushing an object, does it stop moving? Only if there is friction! In the absence of any net external force, an object will keep moving at a constant speed in a straight line, or remain at rest. Copyright 2010 Pearson Education, Inc.

18 Newton s First Law of Motion If you stop pushing an object, does it stop moving? Only if there is friction! In the absence of any net external force, an object will keep moving at a constant speed in a straight line, or remain at rest. This is also known as the law of inertia. Copyright 2010 Pearson Education, Inc.

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20 Newton s First Law Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

21 Newton s First Law Simply stated objects at rest tend to stay at rest, objects in motion stay in motion. More properly, A body acted on by no net force moves with constant velocity and zero acceleration. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

22 First law: Every body remains in a state of rest or uniform motion (constant velocity) unless it is acted upon by an external unbalanced force. This means that in the absence of a non-zero net force, the center of mass of a body either remains at rest, or moves at a constant speed in a straight line.

23 Newton s First Law The figure shows an unbalanced force causing an acceleration and balanced forces resulting in no motion. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

24 Inertial frames of reference When a car turns and a rider continues to move, the rider perceives a force. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

25 Inertial frames of reference When a car turns and a rider continues to move, the rider perceives a force. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

26 Newton s Second Law of Motion Example of a free-body diagram: Copyright 2010 Pearson Education, Inc.

27 Newton s Second Law of Motion Two equal weights exert twice the force of one; this can be used for calibration of a spring: Copyright 2010 Pearson Education, Inc.

28 Newton s Second Law of Motion Now that we have a calibrated spring, we can do more experiments. Acceleration is proportional to force: Copyright 2010 Pearson Education, Inc.

29 Newton s Second Law of Motion Acceleration is inversely proportional to mass: Copyright 2010 Pearson Education, Inc.

30 Newton s Second Law of Motion Combining these two observations gives Or, more familiarly, Copyright 2010 Pearson Education, Inc.

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32 Newton s Second Law of Motion An object may have several forces acting on it; the acceleration is due to the net force: Copyright 2010 Pearson Education, Inc.

33 5-3 Newton s Second Law of Motion Copyright 2010 Pearson Education, Inc.

34 Second law: A body of mass m subject to a net force F undergoes an acceleration a that has the same direction as the force and a magnitude that is directly proportional to the force and inversely proportional to the mass, i.e., F = ma. Alternatively, the total force applied on a body is equal to the time derivative of linear momentum of the body.

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38 An object undergoing uniform circular We have already seen the centripetal acceleration. But, if we measure the mass in motion, Newton s Second Law allows us to calculate the centripetal force. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

39 Using the Second Law Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

40 g, and hence weight, is only constant on earth, at sea level On Earth, g depends on your altitude. On other planets, gravity will have a different value. An object will have a different apparent weight in a rapidly stopping car. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

41 Newton s Third Law of Motion Forces always come in pairs, acting on different objects: If object 1 exerts a force on object 2, then object 2 exerts a force on object 1. These forces are called action-reaction pairs. Copyright 2010 Pearson Education, Inc.

42 Newton s Third Law of Motion Some action-reaction pairs: Copyright 2010 Pearson Education, Inc.

43 The Vector Nature of Forces: Forces in Two Dimensions The easiest way to handle forces in two dimensions is to treat each dimension separately, as we did for kinematics. Copyright 2010 Pearson Education, Inc.

44 Weight The weight of an object on the Earth s surface is the gravitational force exerted on it by the Earth. Copyright 2010 Pearson Education, Inc.

45 Weight Apparent weight: Your perception of your weight is based on the contact forces between your body and your surroundings. If your surroundings are accelerating, your apparent weight may be more or less than your actual weight. Copyright 2010 Pearson Education, Inc.

46 Normal Forces The normal force is the force exerted by a surface on an object. Copyright 2010 Pearson Education, Inc.

47 Normal Forces The normal force may be equal to, greater than, or less than the weight. Copyright 2010 Pearson Education, Inc.

48 Normal Forces The normal force is always perpendicular to the surface. Copyright 2010 Pearson Education, Inc.

49 Newton s Third Law Exerting a force on a body results in a force back upon you. For every action there is an equal and opposite reaction. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

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51 Newton s Third Law Objects at rest An apple on a table or a person in a chair there will be the weight (mass pulled downward by gravity) and the normal force (the table or chair s response). Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

52 Newton s Third Law Objects in motion An apple falling or a refrigerator that needs to be moved the first law allows a net force and mass to lead us to the object s acceleration. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

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56 Free-body diagrams A sketch accounting of forces Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

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59 Many have asked how lethal is a coin dropped from atop a tall building? Urban legends have said that a penny dropped from the top of the Empire State Building can kill. Copyright 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley