1、Chapter 5 Applications of Newtons LawSec.5-1 Force LawsSec.5-2 Tension and normal forcesSec.5-3 Friction forcesSec.5-4 The dynamics of uniform circular motionSec.5-5 Time-dependent forceSec.5-6 Noninertial frames and pseudoforces Sec.5-7 Limitations of Newtons lawSec.5-1 Force Laws Physicists have t
2、raditionally identified four basic forces:(1)the gravitational force(2)the electromagnetic force(3)the weak nuclear force,which causes certain radioactive decay processes and certain reactions among the fundamental particles.(4)the strong force,which operates among the fundamental particles and is r
3、esponsible for binding the nucleus together.Two protons in typical nucleus,for example,the relative strength of these forces would be:strong(relative strength=);electromagnetic();weak();gravitational().21038109101In fact,everything we study about ordinary mechanical systems involves only two force:g
4、ravity and electromagnetism.Tension forcesFriction forcesNormal forcesSec.5-2 Tension and normal forces(张力与压力)(1)Tension force(such as in a stretched rope or string),arises because each small element of the string pulls on the element next to it.mIf the mass of the rope is negligible,the values of t
5、he force exerted on the two ends of the rope must be nearly equal to each other.(2)Normal force:Just like tension force,the normal force is also contact force.Both tension and normal forces originate with the atoms of each body-each atom exerts a force on its neighbor.They belong to electromagnetic
6、forces.NN5-7 In a system,a block(of mass m1=9.5 Kg)slides on a frictionless plane inclined at an angle .The block is attached by a string to a second block(of mass m2=2.6 Kg).The system is released from rest.Find the acceleration of the blocks and the tension in the string.Sample problem:34=m2Sec.5-
7、3 Friction forcesFriction is the force that opposes(反抗)the relative motion or the trend of relative motion of two solid surfaces in contactFrictionstatic frictionkinetic frictionsliding frictionrolling friction1)The forces of static friction(静摩擦力)The frictional forces acting between surfaces at rest
8、 with respect to each other.The maximum force of static friction will be the same as the smallest applied forces necessary to start motion.Fig 5-12 Friction forcefsMaxrestmovingFriction force can be measured by following expt.kfsfThe maximum force of static frictionbetween any pair of dry unlubricat
9、ed surface follows these two empirical laws:(1)It is approximately independent of the area of contact surfaces.(2)It is proportional to the normal force(5-7)where N the magnitude of the normal force,the coefficient of static friction,the maximum force of static friction.sssMaxfN=sMaxfsMaxfssMaxff 2)
10、The force of kinetic friction(动摩擦力,（滑动）):(5-8)where is the coefficient of kinetic friction.Nfkk=kkkssUsually,for a given pair of surfaces .The actual value of and depend on the nature of both the surfaces in contact.SurfaceRubber on dry concrete1.00.8Glass on glass0.9 1.00.4Steel on steel0.60.6Wood
11、on wood0.25 0.50.2 Waxed wood ski on dry snow0.040.004skTable 5-1 some representative values of and .ksSample problem:5-10 Repeat Sample Problem 5-7,taking into account a frictional force between block 1(m1)and the plane.Use the values =0.24 and =0.15.Find the acceleration of the blocks and the tens
12、ion in the string.skm2m1=9.5 Kgm2=2.6 Kg34=Sec.5-4 The dynamics of uniform circular motion1)The conical pendulum(锥摆锥摆)mgmTLmvRFig 5-18Fig 5-18 shows a conical pendulum,as the mass m is revolving in a horizontal circle with constant speed v,the string L sweeps over the surface of an imaginary cone.Ca
13、n we find the period of the motion?)sinLR(=mgT=cosRmvmaTr/sin2=(5-12)(5-13)If we let t represent the time for one complete revolution of the body,then t is called the period of motion.tanRgv=gLgRvRtcos2tan22=2)The banked curveLet the block in Fig 5-20 represent an automobile or railway car moving at
14、 constant speed v on a level roadbed around a curve having a radius of curvature R.Fig 5-20 cRvvWhere does the centripetal force come from?a):sidewise frictional force exerted by the road on the tires.RmvN/sin2=a)b)b):mgN=cosRgv/tan2=Example 1 Example 2 See See 动画库动画库/力学夹力学夹/2/2-0202牛顿定律例题牛顿定律例题.exe
15、.exe 例3Problem:A child whirls a stone in a horizontal circle 1.9 m above the ground by means of a string 1.4 m long.The string breaks,and the stone flies off horizontally,striking the ground 11m away.What was the centripetal acceleration of the stone while in circular motion?Sec.5-5 Time-dependent f
16、orceFor simplicity,we assume here that the forces and the motion are in one dimension,which we take to be the x direction.Then(5-18)dtdvmma(t)(t)Fx=dtmtFdvxx)(=If the forces are dependent on time,we can still use Newtons laws to analyze the motion.xv0dtmtFdvtxvvxxx=0)(0+=txxdttFmvtv00)(1)(=txxF(t)dtmvv001xv(5-19)where is initial velocity,is the velocity at time t.If is a constant,Eqs.19 and 20 will reduce to the formula we obtained for const.acceleration motion.xF+=txdttvxtx00)()(5-20)In the sam