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College Physics (II)

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  1. College Physics (II) Qingxu Li Tel: 62471347, Email: Room 306, College of Mathematics and Physics

  2. “The most incomprehensible thing about the universe is that it is comprehensible.” —-Albert Einstein

  3. About the Course • College Physics (II) • Textbook: General Physics, Bin Liang, et al. • Contents: Mechanics, Oscillation and Wave, Optics; Electromagnetism, Relativity, Quantum Physics, etc. • Course grade: Final Exam (70%) + Performance (30%) • Exercises and Exam are to be finished in English (Chapter 2-7, 10)

  4. Reference books a. Principle of Physics, 3rd edition, Serway and Jewett b. Feynman’ Lectures on Physics (Volume I), by R. P. Feynman c. 物理学,马文蔚,高等教育出版社,第五版 ……

  5. A Brief Summary of Chapter 1

  6. Units, Dimension, Significant Figures, Order of Magnitude, Vector (单位,量纲,有效数字,数量级,矢量) a. Units are indispensable for physical quantities. b. Vectors are to be distinguished from scalars. c. Properties of Vectors: magnitude, direction, components, equality, addition, dot product, cross product, etc.

  7. Position and Displacement Vectors (位置矢量和位移矢量) path 路程,路线 locus 轨迹 distance 距离

  8. Average Velocity and Instantaneous Velocity (平均速度和瞬时速度)

  9. Fig 1.1 A particle moving in the xy plane

  10. Alternative Expressions (其他形式)

  11. Acceleration (加速度) The average acceleration of a particle over a time interval is defined as: And the instantaneous acceleration is defined as:

  12. Alternative Expressions

  13. Fig 1.2The Velocity-Time diagram. The magnitude of acceleration vector is the slope of the curve v—t.

  14. Problems Related to Kinematics

  15. Mechanics • Kinematics • Dynamics

  16. Part II Dynamics The Laws of Motion (运动定律)

  17. Nature and nature’s laws lay hid in night. God said: Let Newton be! and all was light. --Alexander Pope

  18. The Concept of Force (力的概念) The force is a vector quantity. The unit of force is newton, which is defined as the force that, when acting on a 1-kg mass, produces an acceleration of 1m/s2. The dimension of force is:

  19. Newton’s First Law (牛顿第一定律) Newton’s first law of motion: In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line) (在没有外力的情况下,静止的物体会保持静止,而运动的物体则保 持运动速度不变,也就是说运动物体做匀速直线运动。) In simpler terms, when no force acts on a body, its acceleration is zero. (简单地讲,如果没有外力作用,物体的加速度为零)

  20. Comments on the First Law • The first law tell us that an object has a tendency to maintain its • original state of motion in the absence of the force. This tendency is • called inertia, and the first law sometimes called the law of inertia. (牛顿第一定律告诉我们物体在不受外力的情况下有一个保持原来的运动状态的 趋势)-称为惯性,因而第一定律有时又被称为惯性定律) 2.Newton’s first law defines a special set of reference frames called inertial frames. An inertial frame of reference is one in which the first law is valid. (利用牛顿第一定律可以定义一类特殊的参照系-惯性系:在惯性系中,第一定律 成立) 3. Inertial mass is the measure of an objects resistance to change in motion in response to an external force. Inertial mass is different in definition from gravitational mass, but they have the same value, so we call them both simply mass. (惯性质量是物体阻止运动状态发生改变能力即惯性大小的量度。惯性质量和引 力质量在定义上不同,但它们具有相同的数值,统称为质量)

  21. Mass and Weight (质量和重量) Mass and weight are two different quantities, and should not be confused with each other. The magnitude of an object is equal to the magnitude of the gravitational force exerted by the planet on which the objects resides. While the mass of an object is the same everywhere. A given object exhibits a fixed amount of resistance to changes in motion regardless of its location. E.g. A person of mass 60 kg on Earth also has a mass of 60 kg on the moon. The same person weighs 588 Newton on Earth, but weighs 98 Newton on the moon.

  22. Newton’s Second Law (牛顿第二定律) Newton’s second law of motion: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. (物体的加速度和它受到的合外力成正比和它的质量成反比) net force (合力)

  23. Net Force The net force is also known as: • the resultant force • the sum of the force • the total force • the unbalanced force

  24. The Mathematical Form of the Second Law (第二定律的数学形式)

  25. Comments on the Second Law • The Newton’s second law is the central rule of classical mechanics, • which bridges dynamics and kinematics and tells that force is the • cause of the change of motion (not motion!). 2. The second law has an alternative expressions: In special relativity, the mass of an object will vary with its velocity and thus vary with time. The previous form is invalidated in this case but the new form still holds. Of course, both form are equivalent for non-relativistic cases. 3. The second law can also be expressed as:

  26. Newton’s Third Law (牛顿第三定律) Newton’s third law of motion: If two objects interact, the force exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1. (如果两个物体之间(存在)相互作用),则物体 1 作用到物 体 2 上的力和物体 2 作用到物体1上的力大小相等,方向相反) Forces always occurs in pairs, i.e., that a single isolated force cannot exist. (力总是成对出现,也就是说,单个孤立的力是不能存在的)

  27. Comments on the Third Law The force that object 1 exerts on object 2 may be called action force and the force of object 2 on object 1 the reaction force. The action force is equal in magnitude to the reaction force and opposite in direction. In all cases, the action and the reaction forces act on different objects and must be of the same type. (物体 1 作用在物体 2 上的力可以称作作用力,相应地我们称物体 2 作用在物体1上的力为反作用力。作用力和反作用力大小相等方向相反。 作用力和反作用力类型相同,并且作用在不同的物体上)

  28. Applications of Newton’s Law (牛顿定律的应用)

  29. The Particle in Equilibrium (处于平衡状态的质点) Objects that are either at rest or moving with constant velocity are said to be in equilibrium. From Newton’s second law, this condition of equilibrium can be expressed as: (我们称静止或作匀速直线运动的物体处于平衡状态。根据牛顿第二定律,物体 处于平衡状态的条件可以表达为:) or:

  30. The Accelerating Particle (加速质点) When a nonzero net force is acting on a particle, the particle is accelerating, and the second law tell us: (如果质点受到一个非零的合外力,则质点加速运动,由第二定律可知) In practice, the above equation is broken into components, so that two or three equations can be handled independently. (上述方程在应用的时候通常分解为分量形式,这样就可以单独处理两个或 三个方程)

  31. The Atwood Machine (阿特伍德机) E.g. 1.1 When two objects with unequal masses are hung vertically over a light, frictionless pulley as in the figure, the arrangement is called an Atwood machine. The device is sometimes used in the lab to measure the free-fall acceleration. Calculate the magnitude of the acceleration of the two objects and the tension in the string. Fig 1.10 The Atwood machine.

  32. Forces of Friction (摩擦力) When an object moves either on a surface or through a viscous medium such as air or water, there is resistance to the motion. We call such resistance a force of friction. force of static friction force of kinetic friction (静摩擦力) Force of friction (动摩擦力)

  33. Simplified model for force of friction • The magnitude of the force of static friction between any two • surfaces in contact can have the values μs: the coefficient of static friction n: the magnitude of normal force 2. The magnitude of the force of kinetic friction acting between two surfaces is μk: the coefficient of kinetic friction 3. The values ofμk andμs depend on the nature of the surfaces, but the former is generally less than the latter. 4. The direction of the friction force on an object is opposite to the actual motion or the impending motion of the object relative to the surface with which it is in contact.

  34. Fig 1.5 A graph of the magnitude of the friction force versus that of the applied force.

  35. The Gravitational Force: Newton’s Law of Universal Gravitation 引力:牛顿万有引力定律 Newton’s Law of Universal Gravitation Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.

  36. The electrostatic force Coulomb’s Law The magnitude of the electrostatic force between two charged particle separated by a distance r is: The Coulomb constant

  37. The Fundamental Forces of Nature (自然界中的力) • The Gravitational Force • The Electromagnetic Force • The Strong Force (The Nuclear force) • The Weak Force (引力) (电磁力) (强力) (弱力)

  38. Newton’s Second Law Applied to a Particle in Uniform Circular Motion A particle moving in a circular path with uniform speed experiences a centripetal acceleration of magnitude: The acceleration vector is directed toward the centre of the circle and is always perpendicular to its velocity. Apply Newton’s second law to the particle along the radial direction: centripetal force (向心力)

  39. Non-uniform Circular Motion For non-uniform circular motion, there is, in addition to the radial component of acceleration, a tangential component, that is: The total force exerted on the particle is The first term in the RHS is directed toward the center of the circle and is responsible for the centripetal acceleration; and the second term is tangent to the circle and responsible for the tangential acceleration, which causes the speed of the particle to change with time.

  40. Energy of a System (物理体系的能量) kinetic energy potential energy Energy (动能) (势能)

  41. Work(功) The work done by a force on a system is defined as: (作用在一个体系上的力对体系作功定义为) For a finite displacement, (对于一个有限位移)

  42. Work Done by a Constant Force (恒力作功) For a constant force, the work reads: If the applied force is parallel to the direction of the displacement, And if the force is perpendicular to the displacement, then

  43. From the definition of dot product, we get:

  44. Work done by a Spring Hooke’s Law

  45. The work done by the restoring force on a block connected with a spring reads: restoring force 回复力

  46. Kinetic Energy (动能) The work done on a system in motion:

  47. Define the kinetic energy of a particle is: From the above definition, we get: Work-kinetic energy theorem (功能定理)