Principles-of-Physics--03Newton-Law-and-applications

1、2021/8/211. Circular motion:2ntvdvaaanrdtrvrdtdsdtd22dtddtd22rRvardtdvant，O OPOPOvvv2. Relative velocity:2021/8/22Net force: 合力合力Inertia：惯性惯性Viscous：粘性的粘性的Weight: 重量重量Gravitational force: 引力引力Equilibrium: 平衡平衡Cube：立方体立方体Friction: 摩擦摩擦Force of static friction: 静摩擦力静摩擦力Force of kinetic friction: 动摩擦力动

2、摩擦力Pulley：滑轮滑轮Conical pendulum: 圆锥钟摆圆锥钟摆2021/8/231 Newtons First Law Law of Inertia2 Newtons Second Law3 Newtons Third Law4 Solving Problems using Newtons Laws2021/8/24nIn the absence of external forces (or no net force), an object at rest remains at rest, and an object in motion continues in motion

3、 with a constant velocity (with a constant speed in a straight line).The acceleration of an body is zero when no force acts on it. An object has a tendency to maintain its original state of motion in the absence of a force. This tendency is called inertia.Valid in the inertial frames.inertial frames

4、 is one in which Newtons first law is valid. Any reference frame that moves with a constant velocity with respect to an inertial frame is an inertial frame. 1 Newtons First Law Law of Inertia2021/8/25nThe Earth is not an inertial frame because it is connected with two kinds of motions.Orbital motion

5、 about the sun: an 6.0103m/s2Rotational motion about its own axis: an 3.4102m/s2Very small compared with g=9.8m/s2.nIn most situations, we consider a reference frame connected to the Earth as the inertial frame.2021/8/262 Newtons Second LawnThe acceleration of an object is directly proportional to t

6、he net force acting on it and inversely proportional to its mass.An instantaneous relation: once the force acting on an object changes , the acceleration also changes at that moment. Valid for low-speed particles.The component expression:22dvd rFmammdtdtxxyyzzFmaFmaFma2ttnndvvFmamFmamdtIn Cartesian

7、coordinateIn natural coordinatedtvmddtpdF)(2021/8/273 Newtons Third LawnIf two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force F21 exerted by object 2 on object 1.Fab means “the force exerted by a on b”.Remember: the two fo

8、rces in action-reaction pair always act on two different objects, and can not be counteracted.1221FF 2021/8/284 Solving Problems using Newtons Laws1. Isolate the analyzed object. Draw a free-body diagram for each object.nBe sure to include all the forces acting on the object.2. Establish a convenien

9、t reference frame and coordinate system.Problem-Solving Strategy3. For each object, write the equations for Newtons second law in component manner. Generally, the number of unknowns must be equal to the number of equations. If number of unknowns number of equations of Newtons second law, find relati

10、onship between motions. (this situation mostly occurs to many objects whose motions are dependent.)2021/8/294. Solve the equations.5. Check the result by introducing particular or extreme cases of quantities, and compare the results with your intuitive expectations. 2021/8/210Example 1: A small ball

11、 of mass m is attached to the end of a cord of length R, which rotates about a fixed point O in vertical circle under the influence of gravitational force. (initial speed v0) (a) Determine the tension in the cord at any angle .(b) When the ball starts motion in the bottom of the circle, in order to

12、pass point B which is the top of the circle, find the minimum value of initial velocity v0.Solution； Reference frame: the Earth.Coordinate system: natural coordinate. Tangential: Normal： Circular motion:sin (1)dvmgmdt2cos (2)vTmgmR (3)dvRRdt2021/8/211Change the independent variable t to .sindv ddvv

13、dvmgmmmddtdR d00sinvvmvdvmgRd 22011(cos)22mvmvmgRmgRconservation of mechanical energy.20(23cos )mvmgRTRAt the point B, T0, =18020(23)0mvmgRR05vgRVariable force2021/8/212lVelocity-dependent resistive forces1. The medium exerts a resistive force on the object moving through it. 2. The magnitude depend

14、s on the relative speed between the object and the medium. The direction is opposite the direction of motion of the object relative to the medium. 3. Two simplification models: The force is proportional to the velocity. For low speed, small objects The force is proportional to the square of the spee

15、d. For large objects2021/8/213Example 2: In viscous fluid, moving body experiences a resistive force R exerted by the fluid. At low speed:A ball of mass m is released from rest in a liquid. Show the speed of the ball at time t.Solution: Choose down to be positive.Rbv dvmgbvmdt00vtdvdtbgvm/11bt mtTmg

16、veveblnbgvbmtgm vT : terminal velocity; : time constant.Variable force2021/8/214Check the result: The terminal velocity can also be obtained by mg=bvTmgvbWhen1, (1)Ttvve1(1)0.632e/m breflects how fast the body approaches vT/11bt mtTmgveveb2021/8/215xmkgaxomgSolution: (1)coordinate: the released plac

17、e is origin. Down is positive direction.So: x0=0, v0=0, T=kx aconst, variable forcemg kx=mamkAExample 3: The object A (mass m) and a spring (coefficient k) are connected by a light string that passes over a frictionless light pulley. The object is released from rest. At this time, the spring remains

18、 the original length. Find and when the object falls x.va2021/8/216Attention:dxdvva (2) Find v(x)dxxmkgvdv)(xv0022xmkgxvxmkg)()(xvxa(2) (1) wrongaxvv22022222xmkgxaxvdxdvvxa)(2021/8/217Example 4: A pulley system is shown in Figure. The following quantities are known: (1) a the acceleration of pulley

19、A; (2) m1 the mass of block 1; (3) m2 the mass of block 2. The pulleys are modeled as massless and frictionless.Determine the accelerations a1 and a2 of block 1 and 2.Solution: Choose up to be positive.m1:(1)m2:(2)A11 1Tm gm a222Tm gm aUnknown: T, a1, a2.Relationship between m1 and m2: the length l

20、of rope which passes over pulley A is constant.12()()constantlRXxXx1220Xxx122aaa(3)2021/8/218Example 5: An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away. The coefficient of static friction between a person and the wall is . The radius of cylinder is R. (a) What minimum rotational speed is necessary to prevent falling? (b) How m