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- 1. Chapter 4 Dynamics: Newton’s Laws of Motion
- 2. Units of Chapter 4 <ul><li>Force </li></ul><ul><li>Newton’s First Law of Motion </li></ul><ul><li>Mass </li></ul><ul><li>Newton’s Second Law of Motion </li></ul><ul><li>Newton’s Third Law of Motion </li></ul><ul><li>Weight – the Force of Gravity; and the Normal Force </li></ul>
- 3. Units of Chapter 4 <ul><li>Solving Problems with Newton’s Laws: Free-Body Diagrams </li></ul><ul><li>Applications Involving Friction, Inclines </li></ul><ul><li>Problem Solving – A General Approach </li></ul>
- 4. 4-1 Force A force is a push or pull . An object at rest needs a force to get it moving ; a moving object needs a force to change its velocity . The magnitude of a force can be measured using a spring scale.
- 5. 4-2 Newton’s First Law of Motion Newton’s first law is often called the law of inertia . Every object continues in its state of rest, or of uniform velocity in a straight line, as long as no net force acts on it.
- 6. 4-2 Newton’s First Law of Motion Inertial reference frames : An inertial reference frame is one in which Newton’s first law is valid. This excludes rotating and accelerating frames.
- 7. 4-3 Mass Mass is the measure of inertia of an object. In the SI system, mass is measured in kilograms . Inertia The tendency of a body to maintain its state of rest or motion. Mass is not weight : Mass is a property of an object. Weight is the force exerted on that object by gravity. If you go to the moon, whose gravitational acceleration is about 1/6 g , you will weigh much less. Your mass, however, will be the same.
- 8. 4-4 Newton’s Second Law of Motion <ul><li>1 st Law : If no net force acts, object remains at rest or in uniform motion in straight line. </li></ul><ul><li>What if a net force acts? Do Experiments . </li></ul><ul><li>Find, if the net force F 0 The velocity v changes (in magnitude or direction or both). </li></ul><ul><li>A change in the velocity v ( Δ v ) </li></ul><ul><li> There is an acceleration a = ( Δ v/ Δ t ) </li></ul><ul><li>OR </li></ul><ul><li>A net force acting on a body produces an acceleration! F a </li></ul>
- 9. 4-4 Newton’s Second Law of Motion <ul><li>From experiments: The net force F on a body and the acceleration a of that body are related. </li></ul><ul><li>HOW? Answer by EXPERIMENTS ! </li></ul><ul><ul><li>The outcome of thousands of experiments over hundreds of years: </li></ul></ul><ul><li>a F/m (proportionality) </li></ul><ul><li>We choose the units of force so that this is not just a proportionality but an equation: </li></ul><ul><li>a F/m </li></ul><ul><li>OR: ( total !) F = ma </li></ul>
- 10. 4-4 Newton’s Second Law of Motion <ul><li>Newton’s 2nd Law : F = ma </li></ul><ul><ul><li>F = the net ( TOTAL ! ) force acting on mass m </li></ul></ul><ul><ul><li>m = the mass (inertia) of the object. </li></ul></ul><ul><ul><li>a = acceleration of object. Description of the effect of F </li></ul></ul><ul><ul><li>F is the cause of a . </li></ul></ul><ul><li>To emphasize that the F in Newton’s 2 nd Law is the TOTAL (net) force on the mass m , text writes: </li></ul><ul><li>∑ F = ma </li></ul><ul><li> ∑ = a math symbol meaning sum (capital sigma) </li></ul>
- 11. 4-4 Newton’s Second Law of Motion <ul><li>Newton’s 2nd Law : </li></ul><ul><li> </li></ul><ul><li>∑ F = ma </li></ul><ul><li>Force is a vector , so ∑ F = ma is true along each coordinate axis. </li></ul><ul><li>∑ F x = ma x ∑ F y = ma y ∑ F z = ma z </li></ul><ul><li>ONE OF THE MOST </li></ul><ul><li>FUNDAMENTAL & IMPORTANT </li></ul><ul><li>LAWS OF CLASSICAL PHYSICS!!! </li></ul>Based on experiment! Not derivable mathematically!!
- 12. 4-4 Newton’s Second Law of Motion Newton’s second law is the relation between acceleration and force . Acceleration is proportional to NET force and inversely proportional to mass. (4-1)
- 13. 4-4 Newton’s Second Law of Motion The unit of force in the SI system is the newton (N). Note that the pound is a unit of force , not of mass, and can therefore be equated to newtons but not to kilograms.
- 14. 4-5 Newton’s Third Law of Motion Any time a force is exerted on an object, that force is caused by another object. Newton’s third law : Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first. Law of action-reaction : “Every action has an equal & opposite reaction”. (Action-reaction forces act on DIFFERENT objects!)
- 15. 4-5 Newton’s Third Law of Motion A key to the correct application of the third law is that the forces are exerted on different objects . Make sure you don’t use them as if they were acting on the same object.
- 16. 4-5 Newton’s Third Law of Motion Rocket propulsion can also be explained using Newton’s third law: hot gases from combustion spew out of the tail of the rocket at high speeds. The reaction force is what propels the rocket. Note that the rocket does not need anything to “push” against.
- 17. 4-5 Newton’s Third Law of Motion Helpful notation: the first subscript is the object that the force is being exerted on; the second is the source. This need not be done indefinitely, but is a good idea until you get used to dealing with these forces. (4-2)
- 18. Example 4-5
- 19. 4-6 Weight – the Force of Gravity; and the Normal Force Weight is the force exerted on an object by gravity. Close to the surface of the Earth, where the gravitational force is nearly constant, the weight is :
- 20. 4-6 Weight – the Force of Gravity; and the Normal Force An object at rest must have no net force on it. If it is sitting on a table, the force of gravity is still there; what other force is there? The force exerted perpendicular to a surface is called the normal force . It is exactly as large as needed to balance the force from the object (if the required force gets too big, something breaks!)
- 21. Example 4-6 m = 10 kg The normal force is NOT always equal to the weight!!
- 22. m = 10 kg ∑ F = ma F P – mg = ma Example 4-7
- 23. 4-7 Solving Problems with Newton’s Laws – Free-Body Diagrams <ul><li>Draw a sketch . </li></ul><ul><li>For one object, draw a free-body diagram ( force diagram ) , showing all the forces acting on the object. Make the magnitudes and directions as accurate as you can. Label each force. If there are multiple objects, draw a separate diagram for each one. </li></ul><ul><li>Resolve vectors into components. </li></ul><ul><li>Apply Newton’s second law to each component. </li></ul><ul><li>Solve. </li></ul>
- 24. 4-7 Solving Problems with Newton’s Laws – Free-Body Diagrams When a cord or rope pulls on an object, it is said to be under tension , and the force it exerts is called a tension force .
- 25. Example 4-11
- 26. Example 4-13
- 27. Example 4-14 The advantage of a pulley
- 28. Example 4-15
- 29. Problem 25 <ul><li>Take up as positive! </li></ul><ul><li>m 1 = m 2 = 3.2 kg </li></ul><ul><li>m 1 g = m 2 g = 31.4 N </li></ul><ul><li> Bucket 1: F T1 - F T2 - m 1 g = m 1 a </li></ul><ul><li> Bucket 2: F T2 -m 2 g = m 2 a </li></ul><ul><li>∑ F = ma ( y direction), for EACH bucket separately!!! </li></ul> F T1 F T2 F T2 m 2 g m 1 g a a
- 30. Problem 29 <ul><li>Take up positive! </li></ul><ul><li>m = 65 kg </li></ul><ul><li>mg = 637 N </li></ul><ul><li> F T + F T - mg = ma </li></ul><ul><li> 2F T -mg = ma </li></ul><ul><li> F P = - F T (3 rd Law!) </li></ul><ul><li> ∑ F = ma ( y direction) on woman + bucket! </li></ul> F T F T a F P mg
- 31. 4-8 Applications Involving Friction, Inclines On a microscopic scale, most surfaces are rough. The exact details are not yet known, but the force can be modeled in a simple way. We must account for Friction to be realistic!
- 32. <ul><ul><li>Exists between any 2 sliding surfaces. </li></ul></ul><ul><ul><li>Two types of friction: </li></ul></ul><ul><ul><li>Static ( no motion ) friction </li></ul></ul><ul><ul><li>Kinetic ( motion ) friction </li></ul></ul><ul><ul><li>The size of the friction force: Depends on the microscopic details of 2 sliding surfaces. </li></ul></ul><ul><ul><ul><li>The materials they are made of </li></ul></ul></ul><ul><ul><ul><li>Are the surfaces smooth or rough? </li></ul></ul></ul><ul><ul><ul><li>Are they wet or dry? </li></ul></ul></ul><ul><ul><ul><li>Etc., etc., etc. </li></ul></ul></ul>4-8 Applications Involving Friction, Inclines
- 33. <ul><li>Kinetic Friction : Experiments determine the relation used to compute friction forces. </li></ul><ul><li>Friction force F fr is proportional to the magnitude of the normal force F N between two sliding surfaces. </li></ul><ul><ul><li>DIRECTIONS of F fr & F N are each other!! </li></ul></ul><ul><ul><li>F fr F N </li></ul></ul>F a F fr F N mg a
- 34. For kinetic ( sliding ) friction, we write: <ul><li> k is the coefficient of kinetic friction, and is different for every pair of surfaces. </li></ul><ul><ul><li> k depends on the surfaces & their conditions </li></ul></ul><ul><ul><li> k is dimensionless & < 1 </li></ul></ul>4-8 Applications Involving Friction, Inclines
- 35. 4-8 Applications Involving Friction, Inclines Static friction is the frictional force between two surfaces that are not moving along each other. Static friction keeps objects on inclines from sliding, and keeps objects from moving when a force is first applied.
- 36. <ul><li>Static Friction : Experiments are used again. </li></ul><ul><li>The friction force F fr exists || two surfaces, even if there is no motion. Consider the applied force F a : </li></ul> There must be a friction force F fr to oppose F a F a – F fr = 0 or F fr = F a F a F fr F N mg The object is not moving ∑ F = ma = 0 & also v = 0
- 37. <ul><li>Experiments find that the maximum static friction force F fr (max) is proportional to the magnitude (size) of the normal force F N between the two surfaces. </li></ul><ul><li>DIRECTIONS of F fr & F N are each other!! F fr F N </li></ul><ul><li>Write the relation as F fr (max) = s F N </li></ul><ul><li> s Coefficient of static friction </li></ul><ul><ul><li>Depends on the surfaces & their conditions </li></ul></ul><ul><ul><li>Dimensionless & < 1 </li></ul></ul><ul><ul><li>Always find s > k </li></ul></ul><ul><ul><li> Static friction force: F fr s F N </li></ul></ul>
- 38. 4-8 Applications Involving Friction, Inclines
- 39. The static frictional force increases as the applied force increases, until it reaches its maximum . Then the object starts to move, and the kinetic frictional force takes over. 4-8 Applications Involving Friction, Inclines
- 40. Example 4-16
- 41. Example 4-18
- 42. Example 4-19
- 43. Example 4-20
- 44. 4-8 Applications Involving Friction, Inclines <ul><li>An object sliding down an incline has three forces acting on it: the normal force, gravity , and the frictional force. </li></ul><ul><li>The normal force is always perpendicular to the surface. </li></ul><ul><li>The friction force is parallel to it. </li></ul><ul><li>The gravitational force points down . </li></ul>If the object is at rest, the forces are the same except that we use the static frictional force, and the sum of the forces is zero.
- 45. 4-9 Problem Solving – A General Approach <ul><li>Read the problem carefully; then read it again. </li></ul><ul><li>Draw a sketch, and then a free-body diagram. </li></ul><ul><li>Choose a convenient coordinate system . </li></ul><ul><li>List the known and unknown quantities; find relationships between the knowns and the unknowns. </li></ul><ul><li>Estimate the answer. </li></ul><ul><li>Solve the problem without putting in any numbers ( algebraically ); once you are satisfied, put the numbers in. </li></ul><ul><li>Keep track of dimensions . </li></ul><ul><li>Make sure your answer is reasonable . </li></ul>
- 46. Example 4-21
- 47. F p F fr F N (m 1 +m 2 ) g a a = 1.9 m/s 2 Problem 48 For contact forces analyze forces on the two blocks separately.
- 48. Summary of Chapter 4 <ul><li>Newton’s first law: If the net force on an object is zero, it will remain either at rest or moving in a straight line at constant speed. </li></ul><ul><li>Newton’s second law: </li></ul><ul><li>Newton’s third law: </li></ul><ul><li>Weight is the gravitational force on an object. </li></ul><ul><li>The frictional force can be written: </li></ul><ul><li>(kinetic friction) or (static friction) </li></ul><ul><li>Free-body diagrams are essential for problem-solving </li></ul>

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I have a message for the followers of Rev. Sun Myung Moon; my sincere wish is that read it; pray about it; and then contact me or Tossa Cromwell or Hyung Jun Moon or Kyle Toffey; or someone in Las Vegas where Rev. Moon will shortly die; and that is not my prediction; that is what Hyo Jin Moon tells me: everyday; in tears, as he begs me to save his father from dying as a mortal man. And I am doing the best I can.

Let me give you the short version:

The good news is that Rev. Moon is the prophetic figure known as 'the Faithful and Wise Steward' in Luke and Matthew. The 'meat in due season' he brought us was in his book 'Divine Principle'; and in the position of Joseph 'over the House' as of Pharaoh/Satan he has been the one who fed My Generation in these Last Days in the famine 'not for bread'; but for the Word of God. So far. so good.

The problem is that an angel was sent to my house in 1986 to bring me to New Hope PA and unseal the Revelation of Jesus Christ; which I discovered is the Book of life of the Lamb. And my servant John who my Father Jesus sent to me was done to see if Rev. Moon was watching for the 'Day and the Hour' which i represent as his last barrier to becoming the Messiah from his current position as the Messenger or 'Messiah-to-be'. In other words: he's not there yet. Everyone who tries to stop me from reaching and restoring him before he dies with the Seal I was given stands in the position of Satan; since I alone can give him what he will need to reach the crown of life: which is that of Immortality; as a true Messiah and not just another prophet like John the Baptist; whose body Rev. Moon's own now represents substantially. My Father Jesus would like you all to fulfill your portions of responsibility and make sure Rev. Moon gets this message so I can meet him before he dies; and Hyo Jin Moon from spirit world also begs you to believe what I am saying and please do as my Father Jesus asks since if you do not Rev. Moon will die in the position of John the Baptist and I will become the Messiah by default; which you don't want to happen: or do you?

It's up to you; just remember, now that Judgment has been set upon the earth the Unification Church and it's mission is in severe jeopardy if someone does not act soon; as Rev. Moon is about to die.

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To place Rev,. Moon's life in the position where he may die as a mortal man when the possibility of reaching the position of the Messiah from that of the Messenger in one lifetime would seem to be rather important: don't you think so too? I do; and the angel in this room with me at this very moment does as well.

I hope to hear from you; I have done my work; the rest is up to you: and Bless you in the Name of my Father Jesus; he will be here in 10 months on Christmas Day: if I were you I would do something relatively soon: 'now' would be a very good idea.

The best idea you could ever even dream of: in fact.

In Love; the Mighty God of Jacob

Salvation Rose;

christopher witt diamant