frictionlesssurface-DepartmentofAppliedPhysics-TheHongKong.ppt

1、College Physics-by Dr.H.Huang, Department of Applied Physics,1,College Physics (AP101),Dr.Haitao Huang (黄海涛)Department of Applied Physics, Hong Kong PolyUTel: 27665694; Office: CD613Lecture Notes can be downloaded from http:/ap.polyu.edu.hk/apahthuaTextbooks:Physics for Scientist & Engineers, D.C.Gi

2、ancoli, Prentice HallFundamentals of Physics, D.Halliday et al., John Willey & SonsCollege Physics, A.Giambattista et al., McGraw HillUniversity Physics, H.D.Young et al., PearsonPhysics for Scientist & Engineers, R.D.Knight, PearsonResources:Multimedia Lab: CD706,College Physics-by Dr.H.Huang, Depa

3、rtment of Applied Physics,2,Highly Recommended References:For beginners: Berkeley Physics Course (V.1-5) 力学，赵景员，王淑贤 热力学，王竹溪； 电磁学，赵凯华，陈熙谋； 光学，赵凯华，钟锡华Intermediate: The Feynman Lectures on Physics, R.P.Feynman, et al. Classical Mechanics, H.Goldstein et al. Classical Electrodynamics, J.D.Jackson Quantu

4、m Theory of the Solid State, J.Callaway Principles of Optics, M.Born et al. 分析力学， 电动力学， 热力学与统计物理，王竹溪 量子力学，曾谨言Advanced: Course of Theoretical Physics, (V.1-10), L.D.Landau et al. The Principles of Quantum Mechanics, P.A.M.DiracAssessment Weighting:Continuous Assessment: Lab (and report): 16% Quiz (an

5、d midterm exam): 24%Final Exam: 60% (Minimum requirement: D)Minimum requirement for overall grade: D,College Physics-by Dr.H.Huang, Department of Applied Physics,3,Physics,Classical Mechanics,Electrodynamics,Thermodynamics,Quantum Mechanics,Optics,The fundamentals of physics need to be understood by

6、 anyone who hopes to make a career in the sciences or technology: physicists, engineers, chemists, astronomers, mathematicians, geologist, or biologists. The study of physics uses skills that are useful in other fields as well.,College Physics-by Dr.H.Huang, Department of Applied Physics,4,Essence o

7、f PhysicsClassical Mechanics: Newtons lawElectrodynamics: Maxwells equationsOptics: Fermats principleThermodynamics: First, second and third lawsQuantum Mechanics; Schrdingers equation,College Physics-by Dr.H.Huang, Department of Applied Physics,5,Measurement in Physics:Physics is based on measureme

8、nt of physical quantities. Certain physical quantities have been chosen as base quantities, such as length (长度), time (时间), and mass (质量), each has been defined in terms of a standard (标准) and given a unit (单位) measure, such as meter, second, and kilogram. Other physical quantities are defined in te

9、rms of the base quantities and their standards and units.The standard of one meter is the length of the path traveled by light in vacuum (真空) during a time interval of 1/299,792,458 of a second (1983). The standard of one second is the time taken by 9,192,631,770 vibrations of the light (of a specif

10、ied wavelength (波长) emitted by a cesium-133 atom (1967). The standard of one kilogram is the mass of a platinum-iridium cylinder kept at the International Bureau of Weights and Measures near Paris (1889). A second mass standard is the carbon-12 atom, which has been assigned a mass of 12 atomic mass

11、units (u),Measurement,SI Unit:In 1971, the 14th General conference on Weights and Measures picked seven quantities as base quantities, thereby forming the basis of the International System of Units, abbreviated SI from its French name and popularly known as the metric system. Many SI derived units a

12、re defined in terms of these base units.,College Physics-by Dr.H.Huang, Department of Applied Physics,6,SI Unit:In 1971, the 14th General conference on Weights and Measures picked seven quantities as base quantities, thereby forming the basis of the International System of Units, abbreviated SI from

13、 its French name and popularly known as the metric system. Many SI derived units are defined in terms of these base units. Significant Figures (有效数字)The number of reliably known digits in a number is call the number of significant figures. In general, no final result should have more significant fig

14、ures than the original data from which it was derived. If multiple steps of calculation are involved, you should retain more significant figures than the original data have. However, when you come to the final result, you should round off according to the original data with the least significant fig

15、ures. To express the very large and very small quantities, we use the so called scientific notation. We write numbers in “powers of ten”. One advantage of scientific notation is that it allows the number of significant figures to be clearly expressed. Example: A friend asks to borrow your precious d

16、iamond for a day to show her family. You are a bit worried, so you carefully have your diamond weighed on a scale which reads 8.17 grams. The scales accuracy is claimed to be 0.05 grams. The next day you weigh the returned diamond again, getting 8.09 grams. Is this your diamond?,Measurement,College

17、Physics-by Dr.H.Huang, Department of Applied Physics,7,Measurement,Example: How to estimate the radius of the Earth?Suppose that you watch the Sunset over a calm ocean while lying on the beach, starting a stopwatch just as the top of the Sun disappears. You then stand, elevating your eyes by a heigh

18、t h=1.70m, and stop the watch when top of the Sun again disappears. If the elapsed time on the watch is t=11.1s, what is the radius r of the Earth?The angle between the tangent points A and B is .,College Physics-by Dr.H.Huang, Department of Applied Physics,8,Homework:Horses are to race over a dista

19、nce of 4.0 furlongs. What is the race distance in (a) rods and (b) chains? (1 furlong = 201.168 m, 1 rod = 5.0292 m, and 1 chain = 20.117 m.) The micrometer (1 m) is often called the micron. (a) How many microns make up 1.0 km? (b) What fraction of a centimeter equals 1.0 m? The earth is approximate

20、ly a sphere of radius 6.37106 m. (a) What is its circumference in kilometers? (b) What is its surface area in square kilometers? (c) What is its volume in cubic kilometers? The standard kilogram is in the shape of a circular cylinder with its height equal to its diameter. Show that, for a circular c

21、ylinder of fixed volume, this equality gives the smallest surface area, thus minimizing the effects of surface contamination and wear. (a) Assuming that the density (mass/volume) of water is exactly 1g/cm3, express the density of water in kilograms per cubic meter (kg/m3). (b) Suppose that it takes

22、10 h to drain a container of 5700m3 of water. What is the “mass flow rate”, in kilograms per second, of water from the container? The density of an iron atom is 7.87g/cm3, and the mass of an iron atom is 9.2710-26kg. If the atoms are spherical and tightly packed, (a) what is the volume of an iron at

23、om and (b) what is the distance between the centers of adjacent atoms?,Measurement,College Physics-by Dr.H.Huang, Department of Applied Physics,9,Motion Along a Straight Line,The description of the motion of moving bodies is called kinematics (运动学). Particle (质点) is a physical model that we neglect

24、the size and shape of a body. It is treated as a geometric point. Position (位置):The position x of a particle on an axis locate the particle with respect to the origin, or zero point, of the axis. The position is either positive or negative, according to which side of the origin the particle is on, o

25、r zero if the particle is at the origin. Displacement (位移):The displacement x of a particle is the change in its position: Displacement is a vector (矢量) quantity. It is positive if the particle has moved in the positive direction of the axis, and negative if it has moved in the negative direction.Av

26、erage Velocity (平均速度):The algebraic sign of the average velocity indicates the direction of motion. The average velocity does not depend on the actual distance a particle covers, but instead depends on its original and final positions.,College Physics-by Dr.H.Huang, Department of Applied Physics,10,

27、Motion Along a Straight Line,Average Speed (平均速率):Instantaneous Velocity (瞬时速度):The instantaneous velocity (at a particular time) may be found as the slope (at that particular time) of the graph of x versus t. Speed is the magnitude of instantaneous velocity. Average Acceleration (平均加速度):Instantaneo

28、us Acceleration (瞬时加速度):Constant Acceleration:Basic equations:Free-Fall (自由落体) Acceleration: near the Earths surface:,College Physics-by Dr.H.Huang, Department of Applied Physics,11,Motion Along a Straight Line,Example:The right figures are x(t), v(t), and a(t) plots for an elevator cab that is init

29、ially stationary, then moves upward (which we take to be the positive direction), and then stops.For interval bc, the slope in x(t) plot is constant so that the velocity is constant and the acceleration is zero.For interval ab, the velocity increases linearly with time so that the acceleration is co

30、nstant and positive.For interval cd, the velocity decreases linearly with time so that the acceleration is constant but negative.,College Physics-by Dr.H.Huang, Department of Applied Physics,12,Motion Along a Straight Line,Example:The position of a particle moving on the x axis is given byWhat is th

31、e velocity at t=3.5s (x in meter)? Is the velocity constant, or is it continuously changing? Example:A particles position is given by where x is in meter. (a) Find v(t) and a(t). (b) Is there ever a time when v=0? (c) Describe the particles motion for t0. Example:Spotting a police car, you brake a P

32、orsche from 75 km/h to 45 km/h over a distance of 88 m. (a) What is the acceleration, assumed to be constant? (b) What is the elapsed time? (c) If you continue to slow down with the acceleration calculated in (a), how much time will elapse in bringing the car to rest for 75 km/h? What distance will

33、be covered? (d) Suppose that later, using the acceleration calculated in (a) but a different initial velocity, you bring your car to rest after traveling 200m. What is the total braking time?,College Physics-by Dr.H.Huang, Department of Applied Physics,13,Motion Along a Straight Line,Example:A worke

34、r drops a wrench down the elevator shaft of a tall building. (a) Where is the wrench 1.5 s later?(b) How fast is the wrench falling just then?Example:A pitcher tosses a baseball straight up, with an initial speed of 12m/s. (a) How long does the ball take to reach its highest point?(b) How high does

35、the ball rise above its release point?(c) How long will it take for the ball to reach a point 5.0m above its release point?Concepts:Can an object have zero velocity and still be accelerating?Can an object have constant velocity and still have a varying speed?Can the velocity of an object reverse dir

36、ection when the objects acceleration is constant?Can an object be increasing in speed as its acceleration decreases?,College Physics-by Dr.H.Huang, Department of Applied Physics,14,Motion Along a Straight Line,Homework:You drive on Interstate 10 from San Antonio to Houston, half the time at 56km/h a

37、nd the other half at 89km/h. On the way back you travel half the distance at 56km/h and the other half at 89km/h. What is your average speed (a) from San Antonio to Houston, (b) from Houston to back to San Antonio, and (c) for the entire trip? (d) What is your average velocity for the entire trip? (

38、e) Graph x versus t for (a), assuming the motion is all in the positive x direction. Indicate how the average velocity can be found on the graph. Two trains, each having a speed of 30km/h. are headed at each other on the same straight track. A bird that can fly 60km/h flies off the front of one trai

39、n when they are 60km apart and heads directly for the other train. On reaching the other train it flies directly back to the first train, and so forth. (a) How many trips can the bird make from one train to the other before they crash? (b) What is the total distance the bird travels? A man stands st

40、ill from t=0 to t=5.0min; from t=5.00min to t=10.0min he walks briskly in a straight line at a constant speed of 2.20m/s. What are his average velocity and average acceleration during the time intervals (a) 2.00min to 8.00min and (b) 3.00min to 9.00min? (c) Sketch x versus t and v versus t, and indi

41、cate how the answers to (a) and (b) can be obtained from the graphs. An electron with initial velocity v0=1.50105m/s enters a region 1.0cm long where it is electrically accelerated. It emerges with velocity v=5.70106m/s. What was its acceleration, assumed constant? An object falls from a bridge that

42、 is 45m above the water. It falls directly into a model boat, moving with constant velocity, that was 12m from the point of impact when the object was released. What was the speed of the boat?,College Physics-by Dr.H.Huang, Department of Applied Physics,15,Vectors,Scalars (标量) and Vectors (矢量)Scalar

43、s, such as temperature, have magnitude only. They are specified by a number with a unit and obey the rules of arithmetic and ordinary algebra. Vectors, such as displacement, have both magnitude and direction and obey the special rules of vector algebra. The Sum (Resultant) of Two VectorsTwo vectors

44、a and b may be added geometrically by drawing them to a common scale and placing them head to tail. The vector connecting the tail of the first to the head of the second is the sum vector s. Components (分量) of a VectorThe (scalar) components ax and ay of any two dimensional vector a are given by,whe

45、re is the angle formed from the positive direction of x axis to the direction of a.,a,y,x,College Physics-by Dr.H.Huang, Department of Applied Physics,16,Vectors,Unit-Vector (单位矢量；基矢) Notationi, j, and k are unit vectors whose magnitudes are unity and whose directions are those of the x, y, and z ax

46、es, respectively, in a right-handed coordinate system. A vector a can be written as: Adding Vectors in Component FormSuppose a and b are the vectors to be added, the scalar components of the vector sum r are:Commutative law:Associative law:Subtraction:Vectors and Physical LawsThe laws of physics are

47、 independent of the choice of coordinates.,College Physics-by Dr.H.Huang, Department of Applied Physics,17,Vectors,Multiplying a Vector by a ScalarThe product of a scalar s and a vector v is a new vector whose magnitude is sv and whose direction is the same as that of v is s is positive, and opposit

48、e that of v if s is negative. To divide v by s, multiply v by (1/s). The Scalar (or Dot) Product (标量积) The Vector (or Cross) Product (矢量积)The vector product of a and b is a vector c whose magnitude is in which is the smaller of the angle between the directions of a and b. The direction of c is perpendicular to the plane defined by a and b and is given by a right-hand rule.,