大學(xué)物理（上）課件：Lecture3 Newtonian Mechanics (牛頓力學(xué))

1、University Physics ILecture 3 (第三講)Newtonian Mechanics (牛頓力學(xué))【or Newtonian dynamics (牛頓動力學(xué))】1Q: What is the cause for the change of the status of motion of an object?A: It is the force exerting on it. In chapters 2-4, we have discussed Kinematics(運動學(xué)). In kinematics, forces acting on objects (作用在物體上

2、的力) are not under consideration.In dynamics(動力學(xué)), the effect of forces on objects will be the main concern.University Physics I2Newtonian Mechanics describes the relationship between force and motion based on the laws discovered by British physicist Sir Isaac Newton (1642-1727,明末清初).Chapter 5 Force

3、and Motion IAt very high speeds (an appreciable fraction of the speed of light c), Newtonian mechanics must be replaced by Einsteins special theory of relativity(愛因斯坦狹義相對論). If objects are very small (at atomic 10-10 m or nano 10-9 m scale), Newtonian mechanics must be replaced by quantum mechanics(

4、量子力學(xué)).自然哲學(xué)的數(shù)學(xué)原理1687(康熙年間)University Physics I3ForceForce causes the acceleration of an object (or changes its momentum). Force is a vector quantity with both magnitude and direction.Force can be exerted on an object by other objects, either physically touched(如繩子拉力) or at a distance(如電磁力).University

5、 Physics I4Net Force(凈力)Net force is the sum of all forces on a body. It is an overall effect, not a real force. Principle of superposition(疊加原理) for forceUniversity Physics I5Newtons First Law ( Law of Inertia，慣性定律)Newtons First Law ：Given all forces on a body balance one another, if the body is at

6、 rest (stationary靜止), it stays at rest; if it is moving, it continues to move at constant velocity. In such cases, the body is called in equilibrium(平衡). 6Draw Free-Body Diagram (分析受力圖)In a coordinate system, we represent the body as a dot, each force on the body is a vector arrow with its tail on t

7、he body. External force (外力): A collection of two or more bodies is called a system(質(zhì)點系), and any force on the bodies inside the system from bodies outside the system is called an external force. Internal force(內(nèi)力): are forces between two bodies inside the system. Internal forces cannot accelerate t

8、he system. University Physics I7Sample Problem In a two-dimensional tug-of-war(拉力比賽，拔河), Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of the figure. 8Solution:Force components in x-axis:F.B.D.University Physics I9Force components in y-axis

9、:Therefore,University Physics I10Some Particular Forces1. Gravitational force(引力 or 重力),2. Normal force(法向支撐力or正壓力),3. Frictional force(摩擦力),4. Tension(內(nèi)部張力).General Physics I11The Gravitational ForceMagnitude:Direction: Pointing towards the center of EarthWeight（重量）:The weight W of a body is equal

10、to the magnitude of the gravitational force on the body.University Physics I12The Normal Force (法向支撐力or正壓力)When a body presses against a surface(表面), the surface (even a seemingly rigid surface) deforms(形變) and pushes on the body with a normal force， which is perpendicular to the surface.F.B.D.The s

11、urface deforms這個表面發(fā)生形變The normal force is perpendicular to the surfaceUniversity Physics I13Frictional Force(or friction 摩擦力)This force is directed along the surface, opposite the direction of the intended motion. In ideal cases, to simplify situation, friction is assumed to be negligible (namely “t

12、he surface is frictionless”,稱作“光滑表面”).14Tension (張力)The tension force pulls on a body along a taut cord(繃緊的繩子). The cord is often assumed to be massless and un-stretchable.We usually assume a pulley(滑輪，trolley手推車) to be frictionless and massless.A string has a single tension force .The direction dep

13、ends on the body on which this force acts upon.The tension forces at the two ends of the cord are equal in magnitude15Newtons Second LawThe net force on a body is equal to the product of the bodys mass and the acceleration of the body.The acceleration component along a given orthogonal axis is cause

14、d only by the sum of the force components along that same axis, and not by force components along any other axis.This expression of Newtons 2nd law in the right is what we learned in high school physics.University Physics I16Unit of ForceIn SI, the force unit is newton. General Physics I17MassThe ma

15、ss of a body is an intrinsic characteristic that relates a force on the body to the resulting acceleration.Mass is a scalar. It is a measurement of an objects inertia. The greater an objects mass, the more the object resists being accelerated.University Physics I18Newtons Third LawWhen two bodies in

16、teract, the forces on the bodies from each other are always equal in magnitude and opposite in direction. Third-law force pair:Action (force) equals reaction (force)-作用力等于反作用力General Physics I19Conceptual Question:How dose a horse try to use physics to escape work!University Physics I20Applying Newt

17、ons Laws to solve problemsStep 1: Analyze the forces exerted on the object of the study. Draw its free-body-diagram (畫受力圖)Step 3: Analyze its status of motion(including its v, a) and find out the initial conditions (找出初始條件)University Physics I21Sample Problem 5-3The figure shows a block S (the slidi

18、ng block) with mass M = 3.3 kg. The block is free to move along a horizontal frictionless surface such as an air table. The hanging block H falls as the sliding block S accelerates to the right. The block on the table is connected by a cord that wraps over a frictionless pulley to a second block H (

19、the hanging block), with mass m = 2.1 kg. The cord and pulley have negligible masses compared to the blocks (they are “massless”). 22Find (a) the acceleration of the sliding block, (b) the acceleration of the hanging block, and (c) the tension in the cord.SOLUTION: F.B.D.The Acceleration of block S

20、points to the right; acceleration of block H points downward.University Physics I23x-component of block S:y-component of block H:24Sample Problem 5-4From Eq.1, we can obtain how the speed varies with the angle25From Eq.2, we can obtain how the tension of the cord at the angle of 26General Physics I2

21、7Sample Problem 5.06 Force within an elevator cabF.B.D.Find a general solution for the scale reading, whatever the vertical motion of the cab.University Physics I28The scale reading is University Physics I29(a) Coordinate systems can be arbitrarily (or intentionally) set up to solve physical problem

22、s. (c) Physical phenomena (results or solutions) should be independent on the intentionally selected coordinate systems.物理結(jié)果與怎樣選取坐標(biāo)系應(yīng)該是無關(guān)的！ Setting up rectangular coordinate systems and solving problems(b) But selecting a correct one should be more convenient in solving problems.30Sample ProblemA co

23、rd holds stationary a block of mass m = 15 kg, on a frictionless plane that is inclined at angle = 27F.B.D.We now cut the cord. As the block then slides down the inclined plane (斜面), does it accelerate? If so, what is its acceleration?There is no movement of the sliding block perpendicular to the in

24、clined plane. Therefore, Acceleration must be parallel to inclined plane. Think?31The acceleration points down along the inclined plane.x-component(Method 1) We choose our coordinate system with axes parallel and perpendicular to the inclined plane. The arrangement aligns most forces along axes, sim

25、plifying the force resolving procedureUniversity Physics I32Method-2 Alternatively, We set up our rectangular coordinate system with axes along horizontal and vertical directions.x-componenty-componentxyUniversity Physics I33We get the same answer for acceleration as we did in method-1.x-component(1

26、)xySolving in horizontal-vertical coordinate systemy-component34Inertial Reference Frames(慣性參考系)A reference frame at rest (靜止的)or with constant velocity(或勻速運動的) is an inertial reference frame(慣性參考系).A reference frame with acceleration【有加速度的參考系，including rotating frame(旋轉(zhuǎn)的參考系,即是有向心加速度)】is a non-inert

27、ial reference frame(非慣性參考系) e.g. an accelerating elevator is a non-inertial frame. Observing from a non-inertial reference frame(非慣性參考系), Newtons laws do not hold(牛頓定律不成立) -to discuss it laterGround is usually assumed as an inertial frame, neglecting Earths astronomical motion.University Physics I35

28、As the saying goes: True gold does not fear the fiery 真金不怕火煉？摸著石頭過河？中國是個東方國家，英國是個西方國家China is an eastern country, UK is a western country？我是個巨人？Conclusion：There is no absolute correctness or absolute truth，except this statement (沒有絕對真理). Correctness is relative (真確性都是相對的) 36Observing from a non-iner

29、tial reference frame(非慣性參考系), Newtons laws do not hold(牛頓定律不成立)What does “Newtons laws do hold” mean(牛頓定律成立是什么意思)?If there is a net force, there is an acceleration-有力就有加速度！(無力就無加速度)e.g. Look into Newtons 2nd lawWhat does “Newtons laws do not hold” mean(牛頓定律不成立是什么意思)?2. If there is a net force, there

30、 is no acceleration-有力卻沒加速度(有受到凈力但不動)！1. If there is no force, there is an acceleration-沒力卻有加速度(不受力卻會動)37Observing from a non-inertial reference frame(非慣性參考系), Newtons laws do not hold(牛頓定律不成立)e.g. Look into Newtons 2nd law1. If there is no force, there is an acceleration-沒力有加速度！Bus StopConclusion:

31、without force, but acceleratingi.e. Newtons 2nd law breaksConclusion: without force, but acceleratingi.e. Newtons 2nd law breaks38Observing from a non-inertial reference frame(非慣性參考系), Newtons laws do not hold(牛頓定律不成立)e.g. Look into Newtons 2nd law2. If there is a net force, there is no acceleration

32、-有力沒加速度！AlexBettyCharlesAlex asks : what do you feel on the bottom of your feet?Betty answers: I feel some force acting on the bottom of your feet?Alex: Then why you are not moving to me? Newtons law does not hold?General Physics ITutorial problem 139MmGroundWedgeBlockGiven the inclined surface of the wedge and the ground surface are both frictionless, find accelerations of the wedge and the block with respect to the ground.What about the case that two objects move with a relative accelera