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1、Lesson 7 Newtons laws of motion Everyday experience leads one to the conclusion that the case of motion is force.Children playing with wooden trains or wheeled animals soon find out for themselves that pulling the string attached to the toy will cause the toy to move.In order to move the toy in seve
2、ral different directions it is necessary to push or pull i those different directions.Thus each force has associated with it a given direction.Similarly,each force has associated with it a magnitude-the child can push or pull the toy harder in order to obtain a more positive result.An investigation
3、of dynamics requires a quantified description of motion.Three fundamental kinematical quantities used to describe the motion of a particle are position,velocity,and acceleration.These basic terms are defined with respect to a frame of reference that describes the three-dimensional space within which
4、 the motion occurs.In most situations,the motion of the earth is negligible in comparison to the motion fo the object of interest.The reference frame in such cases may be considered to be attached to the earth.To describe the motion of a particle we must postulate that the reference frame is fixed,t
5、hat is,stationary,in space.Although considering the earth to be fixed in not exactly correct,the errors that result from this assumption are negligible for most systems.This reference frame can be visualize as a set fo rectangular Cartesian axes syz.The laws of motion stated by Sir Isaac Newton(1642
6、-1727)in his historic work Principia(1687)are the foundation of the study of dynamics.The simplest possible motion to discuss is that of a particle moving under the influence of no force.Such a particle is said to be moving freely,and its motion is governed by Newtons first law of motion,i.e.,FIRST
7、LAW:a particle will remain at rest or move with constant speed along a straight line,unless it is acted upon by a resultant force.The magnitude and direction of a given force acting on a given particle can be modeled together as a vector,say F,which will intuitively cause the particle to move.What p
8、roperty of the motion is related to the force?Intuition would certainly lead most readers to argue that the larger the force the faster the particle moves and so to relate the velocity of the particle to the force acting on the particle.This was the common mistake made by mathematicians in the pre-N
9、ewtonian era-a mistake which prevented significant progress in mechanics for many years.It is known that the velocity of a particle varies from one reference frame to another.Hence if the velocity is related to the force,the relationship could only hold in one particular reference frame.Unlike veloc
10、ity,the acceleration of a particle is independent of the reference frame relative to which the acceleration is measured,and so if the acceleration of the particle were related to the force acting on the particle then the relationship would hold in all reference frames rather than in only one particu
11、lar reference frame.This relationship was in fact postulated by Newton and is incorporated in his second law of motion,i.e.,SECOND LAW:when a resultant force is exerted on a particle,the acceleration of that particle is parallel to the direction of the force and the magnitude of the acceleration is
12、proportional to the magnitude of the force.If a particle P of mass m is moving with acceleration a under the action of a force F then according to Newtons second law of motion,ma=F.Newtons second law involves the force acting on the particle.In most cases several different forces will be acting on t
13、he particle simultaneously,and it is therefore necessary to postulate that it is the vector sum of all the individual forces which must be used as the force in applying the second law.This postulate is in agreement with the concept of the resultant of several forces in statics,and the necessity for
14、making such a postulate was first realized by Mach in 1883.Newtons third law of motion can be stated as follows.THIRD LAW:the force exerted on one particle by another is equal and opposite to the force exerted by the first particle on the second.In face,most,forces between particles obey the third law of motion and such forces are sometimes called Newtonian.