Chapter3: Newton's Laws in Motion


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Chapter Three: Newton's Laws of Motion

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Chapter3: Newton's Laws in Motion

  1. 1. Chapter 3 Newton’s Laws of Motion (‫)قوانين الحركة لنيوتن‬
  2. 2. Sir Isaac Newton 1642 – 1727  Formulated basic laws of mechanics (‫صاغ قوانين الميكانيكا‬ ‫)الساسية‬  Discovered Law of Universal Gravitation (‫)اكتشف قانون الجذب العام‬  Invented form of calculus  Many observations dealing with light and optics 
  3. 3. Force  Forces are what cause any change in the velocity of an object (‫)القوة هي اي شيء يغير من سرعة الجسم‬ Newton’s definition  A force is that which causes an acceleration (‫) القوة هي التي تسبب التسارع‬ 
  4. 4. Classes of Forces (‫)اشكال القوى‬  Contact forces(‫ )القوى الغير مجالية‬involve physical contact between two objects   Examples a, b, c Field forces(‫ )قوى المجال‬act through empty space   No physical contact is required Examples d, e, f
  5. 5. Fundamental Forces (‫) القوى الساسية في الطبيعة‬  Gravitational  force (‫)قوة الجاذبية‬ Between objects  Electromagnetic  Between electric charges  Nuclear  force (‫)القوة النووية‬ Between subatomic particles  Weak  forces (‫)القوى الكهرمغناطيسية‬ forces (‫)القوى الضعيفة‬ Arise in certain radioactive decay processes  Note: These are all field forces
  6. 6. More About Forces    A spring can be used to calibrate (‫ )معايرة‬the magnitude of a force Doubling the force causes double the reading on the spring When both forces are applied, the reading is three times the initial reading
  7. 7. Vector Nature of Forces (‫) الطبيعة المتجهة للقوى‬    The forces are applied perpendicularly to each other The resultant (or net) force (‫)القوة المحصلة‬is the hypotenuse (‫)الوتر‬ Forces are vectors, so you must use the rules for vector addition to find the net force acting on an object
  8. 8. Newton’s First Law (‫)قانون نيوتن الول‬  If an object does not interact with other objects, it is possible to identify a reference frame in which the object has zero acceleration   This is also called the law of inertia (‫قانون القصور‬ ‫)الذاتي‬ It defines a special set of reference frames called inertial frames We call this an inertial frame of reference (‫) اطار المرجع للقصور الذاتي‬ 
  9. 9. Inertial Frames (‫اطارات القصور‬ ‫)الذاتي‬   Any reference frame that moves with constant velocity relative to an inertial frame is itself an inertial frame A reference frame that moves with constant velocity relative to the distant stars is the best approximation of an inertial frame  We can consider the Earth to be such an inertial frame, although it has a small centripetal acceleration associated with its motion
  10. 10. Newton’s First Law – Alternative Statement (‫) صيغة اخرى لقانون نيوتن الول‬  In the absence of external forces, when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant velocity   Newton’s First Law describes what happens in the absence of a force  Does not describe zero net force Also tells us that when no force acts on an object, the acceleration of the object is zero
  11. 11. More About Mass is an inherent property (‫ )خاصية متاصلة‬of an object  Mass is independent of the object’s surroundings  Mass is independent of the method used to measure it  Mass is a scalar quantity  The SI unit of mass is kg  Mass
  12. 12. Mass vs. Weight  Mass and weight are two different quantities  Weight is equal to the magnitude of the gravitational force exerted on the object  Weight will vary with location  Example:  wearth = 180 lb; wmoon ~ 30 lb  mearth = 2 kg; mmoon = 2 kg
  13. 13. Newton’s Second Law (‫) قانون نيوتن الثاني‬  When viewed from an inertial reference frame, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass   Force is the cause of change in motion, as measured by the acceleration Algebraically, r aµ  r ∑F m r r → ∑ F = ma With a proportionality constant of 1 and speeds much lower than the speed of light
  14. 14. More About Newton’s Second Law r  ∑ F is the net force  This is the vector sum of all the forces acting on the object  Newton’s Second Law can be expressed in terms of components:    ΣFx = m ax ΣFy = m ay ΣFz = m az
  15. 15. Units of Force (‫وحدات قياس‬ ‫)القوة‬  The  SI unit of force is the newton (N) 1 N = 1 kg·m / s2  The US Customary unit of force is a pound (lb)  1 1 lb = 1 slug·ft / s2 N ~ ¼ lb
  16. 16. Gravitational Force (‫قوة‬ ‫)الجاذبية‬ r  The gravitational force, F , is the force that g the earth exerts on an object  This force is directed toward the center of the earth  From Newton’s Second Law r r  F = mg g  Its magnitude is called the weight of the object  Weight = Fg= mg
  17. 17. More About Weight  Because it is dependent on g, the weight varies with location   g, and therefore the weight, is less at higher altitudes This can be extended to other planets, but the value of g varies from planet to planet, so the object’s weight will vary from planet to planet  Weight object is not an inherent property of the
  18. 18. Newton’s Third Law (‫) قانون نيوتن الثالث‬ r  If two objects interact, the force F exerted by 12 object 1 on object 2 is equal in magnitude r and opposite in direction to the force F21 exerted by object 2 on object 1 r r F12 = −F21   r Note on notation: FAB is the force exerted by A on B
  19. 19. Newton’s Third Law, Alternative Statements (‫)قانون نيوتن الثالث‬    Forces always occur in pairs(‫القوى عادتا تحدث بشكل‬ ‫)ازواج‬ A single isolated force cannot exist The action force is equal in magnitude to the reaction force and opposite in direction    One of the forces is the action force, the other is the reaction force It doesn’t matter which is considered the action and which the reaction The action and reaction forces must act on different objects and be of the same type
  20. 20. Action-Reaction Examples, 1 (‫)الفعل و رد الفعل‬  r The force F12 exerted by object 1 on object 2 is equal in magnitude and opposite in r direction to F21 exerted by object 2 on object 1  r r F12 = −F21
  21. 21. Action-Reaction Examples, 2  The normal force (table on monitor) is the reaction of the force the monitor exerts on the table   Normal means perpendicular, in this case The action (Earth on monitor) force is equal in magnitude and opposite in direction to the reaction force, the force the monitor exerts on the Earth
  22. 22. Free Body Diagram (‫) المخطط البياني للجسم الحر‬  In a free body diagram, you want the forces acting on a particular object   Model the object as a particle The normal force and the force of gravity are the forces that act on the monitor
  23. 23. Free Body Diagram, cont.  The most important step in solving problems involving Newton’s Laws is to draw the free body diagram  Be sure to include only the forces acting on the object of interest  Include any field forces acting on the object  Do not assume the normal force equals the weight
  24. 24. Applications of Newton’s Laws (‫) تطبيقات على قوانين نيوتن‬  Assumptions (‫)الفتراضات‬  Objects can be modeled as particles  Interested only in the external forces acting on the object  can neglect reaction forces  Initially dealing with frictionless surfaces( ‫اسطح عديمة‬ ‫)الحتكاك‬  Masses of strings or ropes are negligible  The force the rope exerts is away from the object and parallel to the rope  When a rope attached to an object is pulling it, the magnitude of that force is the tension in the rope
  25. 25. Particles in Equilibrium (‫) الجسيمات في حالة التزان‬  If the acceleration of an object that can be modeled as a particle is zero, the object is said to be in equilibrium  The model is the particle in equilibrium model  Mathematically, the net force acting on the object is zero  ∑F=0 ∑F x = 0 and ∑F y =0
  26. 26. Equilibrium, Example 1a   A lamp is suspended from a chain of negligible mass The forces acting on the lamp are    the downward force of gravity the upward tension in the chain Applying equilibrium gives ∑F y = 0 → T − Fg = 0 → T = Fg
  27. 27. Equilibrium, Example 1b    T and Fg  Not an action-reaction pair Both on the lamp act    T and T '     T ' and T "    Action-reaction forces Lamp on chain and chain on lamp  Action-reaction forces Chain on ceiling and ceiling on chain Only the forces acting on the lamp are included in the free body diagram
  28. 28. Equilibrium, Example 2a   Example Conceptualize the traffic light    Assume cables don’t break Nothing is moving Categorize as an equilibrium problem   No movement, so acceleration is zero Model as a particle in equilibrium
  29. 29. Equilibrium, Example 2b  Analyze    Need two free-body diagrams Apply equilibrium equation to the light Apply equilibrium equations to the knot
  30. 30. Equilibrium, Example 2 c  Analyze,   cont. Find T3 from applying equilibrium in the y-direction to the light Find T1 and T2 from applying equilibrium in the xand y-directions to the knot  Finalize  Think about different situations and see if the results are reasonable
  31. 31. Particles Under a Net Force  If an object that can be modeled as a particle experiences an acceleration, there must be a nonzero net force acting on it  Model is particle under a net force model  Draw a free-body diagram  Apply Newton’s Second Law in component form
  32. 32. Newton’s Second Law, Example 1a  Forces acting on the crate:    A tension, acting through the rope, is the  magnitude of force T  The gravitational force, Fg  The normal force, n , exerted by the floor
  33. 33. Newton’s Second Law, Example 1b  Apply Newton’s Second Law in component form: ∑F x = T = max ∑F y   = n − Fg = 0 → n = Fg Solve for the unknown(s) If the tension is constant, then a is constant and the kinematic equations can be used to more fully describe the motion of the crate
  34. 34. Note About the Normal Force   The normal force is not always equal to the gravitational force of the object For example, in this case ∑F y  = n − Fg − F = 0 and n = Fg + F   n may also be less than Fg
  35. 35. Multiple Objects (‫اجسام‬ ‫)متعددة‬  When two or more objects are connected or in contact, Newton’s laws may be applied to the system as a whole and/or to each individual object  Whichever you use to solve the problem, the other approach can be used as a check
  36. 36. Multiple Objects, Conceptualize     Observe the two objects in contact Note the force Calculate the acceleration Reverse the direction of the applied force and repeat
  37. 37. Multiple Objects, Example 1     First treat the system as a whole: ∑ Fx = msystemax Apply Newton’s Laws to the individual blocks Solve for unknown(s) Check: |P12| = |P21|
  38. 38. Forces of Friction (‫قوى‬ ‫)الحتكاك‬  When an object is in motion on a surface (‫ )سطح‬or through a viscous medium (‫وسط‬ ‫ ,)لزج‬there will be a resistance to the motion  This is due to the interactions (‫ )تفاعلت‬between the object and its environment (‫)البيئة‬  This resistance (‫ )المقاومة‬is called the force of friction
  39. 39. Forces of Friction, cont.  Friction is proportional to the normal force  ƒs ≤ µs n and ƒk= µk n     μ is the coefficient of friction (‫)معامل التحتكاك‬ These equations relate the magnitudes of the forces, they are not vector equations For static friction, the equals sign is valid only at impeding motion (‫ ,)اعاقة الحركة‬the surfaces are on the verge of slipping (‫)وشك النزلق‬ Use the inequality if the surfaces are not on the verge of slipping
  40. 40. Forces of Friction, final  The coefficient of friction depends on the surfaces in contact  The force of static friction is generally greater than the force of kinetic friction  The direction of the frictional force is opposite the direction of motion and parallel to the surfaces in contact  The coefficients of friction are nearly independent of the area of contact
  41. 41. Static Friction     Static friction acts to keep the object from moving r r If r increases, so does ƒ s F r If F decreases, so does ƒ s ƒs ≤ µs n  Remember, the equality holds when the surfaces are on the verge of slipping
  42. 42. Kinetic Friction    The force of kinetic friction acts when the object is in motion Although µk can vary with speed, we shall neglect any such variations ƒk = µk n
  43. 43. Explore Forces of Friction   Vary the applied force Note the value of the frictional force   Compare the values Note what happens when the can starts to move
  44. 44. Some Coefficients of Friction
  45. 45. Friction in Newton’s Laws Problems  Friction r is a force, so it simply is included in the ∑ F in Newton’s Laws  The rules of friction allow you to determine the direction and magnitude of the force of friction
  46. 46. Friction Example, 1    The block is sliding down the plane, so friction acts up the plane This setup can be used to experimentally determine the coefficient of friction µ = tan θ   For µs, use the angle where the block just slips For µk, use the angle where the block slides down at a constant speed