PHYS 218sec. 517-520ReviewChap. 4Newton’s laws of motionFma=2DynamicsStudies the relationship of motion to the forces that cause it, i.e., the origin of the motion.Newton’s (three) laws of motionClassical Mechanics (Newtonian Mechanics)Contributions fromCopernicusBraheKeplerGalileietcModern PhysicsRelativity Quantum Mechanics3Force & InteractionsForce: an interaction between two bodies or between a body and its environment.(There is no force without source.)A force is a vector quantity.• Contact force: a force which involves direct contact between two bodies¾ Normal force9 exerted on an object by any surface with which it is contact9 always acts perpendicular to the surface of contact¾ Friction force9 exerted on an object by any surface with which it is contact9 acts parallel to the surface in the direction that opposes sliding¾ Tension force9 pulling force exerted by a stretched rope or cord on an object to which it is attached• Long-range force: a force which acts even when the bodies are separated by empty space¾ Gravitational force which gives weight.Macroscopic concept4Superposition of forcesAny number of forces applied at a point on a body have the same effect as a single force equal to the vector sum of the forces12:Decompose the net force inet fonto corcemp n,oentsxxyiyRFRF===++=∑∑∑RF F FJG JGJGJG"Just as you have learned about vector algebraUnit of forceN: Newton See slide number 7 for details.5Newton’s first law of motionA body acted on by no net force moves with constant velocity(which may be zero) and zero acceleration.That means if no change in velocity= ⇒∑F0GGImportant conceptsInertia: the tendency of a body to keep moving once it is set in motion• a property of a bodyEquilibrium: when a body is either at rest or moving with constant velocityThis is the case when =∑F0GGTherefore, it is moving in a straight linewith constant speed6Inertial frame of referenceInertial frameSee Chap. 3Inertial frame of reference: A reference frame where Newton’s first law is valid.If a frame is accelerating, it is not an inertial frame.But if a frame is moving with a constant velocity with respect to an inertial frame, it is also an inertial frame.Inertial frame0a ≠Non-inertial frame0, 0va≠ =Inertial frame7Newton’s second law of motionm=∑FaGGExperimental observationMagnitude of the net force is proportional to the magnitude of the acceleration of the object∝∑FaGGYou can write this relation to an equation by using a proportionality constant, mm=∑FaGGm is called mass; in fact, this defines massThis defines the unit of force: Newton (N)1 Newton: the amount of force that gives an acceleration of 1 m/s2to a body of 1kg. 21N=1kgm/s⋅8Inertial massNewton’s 2nd law gives a way to measure masses.Suppose you have two objects with masses m1and m2. Assume that you know the mass m1, then you can measure m2by applying a constant net force to both objects.111 2 2 2 12Since the applied net force is equal, Newton's 2nd law givesama ma m ma= ⇒ =Masses determined in this way are called inertial masses.9Using Newton’s Second Law• Newton’s 2ndlaw is written as a vector equation.• Consider all forces and write the net force in component form.• Then each component satisfies Newton’s 2ndlaw.• Only external forces should be considered.• The above form of Newton’s 2ndlaw is valid only when the mass m is constant.• Newton’s laws are valid only within an inertial frame.• ma is not a force. It is the result of the force applied. Therefore, it should not appear in free-body diagrams.,,xxyyzzFma Fma Fma===∑∑∑10Mass and weightWeight of a body: the gravitational forcethat the earth exerts on the bodyThis is the force that makes the body accelerate downward.This force should be considered in most problems in Chap. 4 and 5.A body with mass m have weight of which magnitude w is given byweight is a force, so vectorit is a m∴ =wgGGwmg=w: magnitude of weight, always positiveg: gravitation acceleration constant, always positiveTherefore, if you choose upward as your positive y-direction, since weight directs always downward, you have –mg for weight.Weight also provides a way to measure masses,1212since is equal.wwgmm=Gravitational massMass: scalar quantity11Newton’s third law of motionIf body A exerts a force on body B (this is an action), then body B exerts a force on body A (this is a reaction). These two forces have the same magnitude but are opposite in directionon on ABBA= −FFGGIMPORTANT!These two forces act on different bodies!action-reaction pairSolve examples and problemsin the
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