1 / 80

Introduction Chapter

Introduction Chapter. Dr. Yousef Abou-Ali yabouali@iust.edu.sy. 1.3 Standards and Units. Introduction Chapter. 1.7 Vectors and Vector Addition. 1.10 Products of Vectors. 4.2 Newton's First Law. 4.3 Newton's Second Law. 4.5 Newton's Third Law. Dr. Y. Abou-Ali, IUST.

gari
Télécharger la présentation

Introduction Chapter

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction Chapter Dr. Yousef Abou-Ali yabouali@iust.edu.sy

  2. 1.3Standards and Units Introduction Chapter 1.7Vectors and Vector Addition 1.10Products of Vectors 4.2Newton's First Law 4.3Newton's Second Law 4.5Newton's Third Law Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  3. To know standards and units and be able to do unit conversions. • To be able to add vectors. • To be able to break down vectors into x and y components. • To be able to calculate dot and cross products. • To understand force – either directly or as the net force of multiple components. • To study and apply Newton’s First Law. • To study and apply the concept of mass and acceleration as components of Newton’s Second Law. • To differentiate between mass and weight. • To study and apply Newton’s Third Law. Goals for Introduction Chapter Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  4. Two Reasons: • Physics is one of the most fundamental of the science. Why We Study Physics? • The study of physics is an adventure. If you wondered: why the sky is blue, why radio waves travel through empty space and how a satellite stays in orbit? You can not find the answers without first understanding the basic laws of physics. Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  5. Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns and principles that relate these phenomena. Introduction • Example:Galileo dropped light and heavy objects from the top of the Leaning Tower of Pisa to find out whether their rates of fall were the same or different. Galileo recognized that only experi- mental investigation could answer this question.From examining the results of his experiments he made the inductive leap to the principle, or theory, that the acceleration of a falling body is independent of its weight. • Every physical theory has a range of validity outside of which it is not applicable. Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  6. Introduction • Getting back to Galileo, suppose we drop a feather and a cannonball. They certainly do not fall at the same rate. This does not mean that Galileo was wrong; it means that his theory was incomplete. If we drop the feather and the cannonball in a vacuum to eliminate the effects of the air, then they do fall at the same rate. Galileo's theory has a range of validity .

  7. Introduction Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  8. Introduction • At some points in their studies, almost all physics students find themselves thinking “ I understand the concepts but I just cant solve the problems”. You do not know physics unless you can do physics. Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  9. Physics is an experimental science, Experiments require measurements. • We use numbers to describe the results of measurements (any number used to describe a physical phenomena quantitatively is a called physical quantity). 1.3Standards and Units Example:twophysical quantities that describe you, are your weight and height . • Some physical quantities are so fundamental that we can define them only by describing how to measure them. Such a definition is called an operational definition. Examples:measuring a distance by using a rule, and measuring a time interval by using a stopwatch. Dr. Y. Abou-Ali Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  10. 1.3Standards and Units • When we measure a quantity, we always compare it with some reference standard. Such a standard defines a unit of the quantity. • To make accurate, reliable measurements, we need units of measurements that do not change. The system used by scientists and engineers around the world called the “metric system” but since 1960 known as International System or SI. Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  11. 1.3Standards and Units • There are three fundamental SI Units: • Time • Second (s) • Length • Meter (m) • Mass • Kilogram (kg) Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  12. The Second • Originally tied to the length of a day. 1.3Standards and Units • Now, exceptionally accurate. • Atomic clock • 9,192,631,770 oscillations of a low-energy transition in Cs • In the microwave region Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  13. 3 The meter 1.3Standards and Units Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  14. 3 The meter • Now tied to Kr discharge and counting a certain number of wavelengths. 1.3Standards and Units • Exceptionally accurate, in fact redefining c, speed of light. • New definition is the distance that light can travel in a vacuum in 1/299,792,458 s. • So accurate that it loses only 1 second in 30 million years. Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  15. 3 The kilogram • The kilogram, defined to be the mass of a particular cylinder of platinum-iridium alloy. 1.3Standards and Units Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  16. 3 1.3Standards and Units Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  17. 3 1.3Standards and Units Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  18. 1.3Standards and Units The British System: • Length:1inch= 2.54cm. • Force: 1 pound = 4.448221615260 newtons. • For time, the British unit is second. • British units are used only in mechanics and thermodynamics. No BU for electrical units. Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  19. Dimensional analysis The word dimension has a special meaning in physics. It denotes the physical nature of a quantity. Whether a distance is measured in units of feet or meters or fathoms, it is still a distance. We say its dimension is length. • The symbols we use in this book to specify the dimensions of length, mass, and • time are L, M, and T, respectively. We shall often use brackets [ ] to denote the dimensions of a physical quantity. For example, the symbol we use for speed in this book is v, and in our notation the dimensions of speed are written [v] = L/T.

  20. Dimensional analysis • Dimensional analysis makes use of the fact that dimensions can be treated as algebraic quantities. For example, quantities can be added or subtracted only if they have the same dimensions. • For example we can Show that the expression v = at is dimensionally correct, where v represents speed, a acceleration, and t an instant of time. So by used dimensional analysis we write • [V]= L/T • And

  21. Dimensional analysis • Example : Analysis of a Power Law • Suppose we are told that the acceleration a of a particle • moving with uniform speed v in a circle of radius r is proportional to some power of r, say rn, and some power of v, say vm. Determine the values of n and m and write the simplest form of an equation for the acceleration. • Solution : • Let us take a to be

  22. Dimensional analysis • where k is a dimensionless constant of proportionality. • Knowing the dimensions of a, r, and v, we see that the dimensional equation must be This dimensional equation is balanced under the conditions n+m = 1 and m=2 Therefore n=-1 , and we can write the acceleration expression as

  23. Dimensional analysis • which of the following equations are dimensionally correct ? • (a) • (b) • Solution : • (a) This is incorrect since the units of [ax] are m2/s2 , while the units of [v] are m/s . • (b) This is correct since the units of [y] are m, and cos (kx) is dimensionless if [k] is in m−1.

  24. Dimensional analysis • Newton’s law of universal gravitation is represented by • Here F is the magnitude of the gravitational force exerted by one small object on another, M and m are the masses of the objects, and r is a distance. Force has the SI units kg·m/s2. • What are the SI units of the proportionality constant G?

  25. Dimensional analysis

  26. Time, temperature, mass, density…. Can be describe by a single number with unit. • Some important physical quantities have a direction associated with them and cant be describe by a single number. 1.7 Vectors and Vectors Addition • Example: motion of airplane. • Physical quantity is described by a single number we call it ascalar quantity. For scalar number 6 kg + 3 kg = 9 kg. • Vector quantityhas both a magnitude (how much or how many)and directionin space. To combine vectors require different set of a operation. • Simplest vector quantity is Displacement (change in position of a point). Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  27. P2 P1 • Change from P1 to P2 represent by line from P1 to P2 1.7 Vectors and Vectors Addition • We write vector quantity such as displacement: • In the book vector symbols are boldface italic type with an arrow above them. • Displacement is not related directly to the total distance travelled. Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  28. Anti parallel vectors Parallel vectors • Magnitude of 1.2 • In the “world of vectors” 1+1 does not necessarily equal 2. • Graphically? 1.7 Vectors and Vectors Addition Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  29. where are called the components vectors of vector Components of Vectors Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  30. We need a single number to describe • When the component vector points in the positive x-direction, we define the number Ax to be equal to the magnitude of • When the component vector points in the negative x-direction, we define the number Ax to be equal to the negative of that magnitude. • We can calculate the components of if we know its magnitude and direction, we will describe the direction of a vector by its angle. • In last figure θ (theta) is the angle between and +x axis. Components of Vectors • The magnitude of a vector quantity always positive (never negative). Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  31. y θ cx(-) x 0 By(+) θ cy(-) x 0 y Bx(-) Components of Vectors • We measured θ from +x axis toward +y axis. Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  32. a. What are the x- and y- components of vector In the figure (a) below? The magnitude of the vector is D = 3.00 m and the angle α = 45o. b. What are the x- and y- components of vector In the figure (b) below? The magnitude of the vector is E = 4.50 m and β = 37.0o. y Dx(+) x α Dy(-) (a) Example 1.6(Finding Components): Components of Vectors Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  33. Execute:the angle between and +x axis is α (alpha) Solution: a)Identify and step:all we need Eqs (1.7), the angle is not measured from +x toward +y axis. Components of Vectors θ = - α = - 45o Dx = D cos θ = (3m)(cos(-45o)) = 2.1 m Dy = D sin θ = (3m)(sin(-45o)) = - 2.1 m Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  34. b)x is not horizontal & y is not vertical. The angle β (beta) is between and +y axis, we cant use Eqs 1.7. is the hypotenuse of a right triangle and the other side are Ex & Ey. Components of Vectors Ex= E sin β = (4.50 m)(sin(37.0o)) = 2.71 m Ey= E cos β = (4.50 m)(cos(37.0o)) = 3.59 m Evaluate:if you want to use Eqs 1.7 you have to find the angle between +x and vector E. θ = 90o – 37o = 53o Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  35. y x 0 (1.13) • A unit vector that has magnitude of 1 with no unit. Unit Vectors Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  36. When we have two vectors Unit Vectors Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  37. If we have third unit k: Unit Vectors Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  38. Given the two displacement: Find the magnitude of the displacement: Identify, step and execute:Letting: Example 1.9(Using Unit Vectors): Unit Vectors Solution: Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  39. The unit of are m the components also are in m. Unit Vectors Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  40. The scalar product of is donated by Definition of the scalar (dot) product Work Displacement Force Scalar Product: 1.10Products of Vectors • Also called dot product. Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  41. Commutative law Scalar (dot) product in terms of components 1.10Products of Vectors • Scalar product, find the angle Φ between any two vectors whose components are known. Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  42. Find the scalar product Of the two vectors in the figure below. The magnitude of the vectors are A = 4.00 and B = 5.00 y 130.0o Φ 53.0o x Example 1.10(Calculating a Scalar Product): 1.10Products of Vectors Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  43. Positive because Φ between 0 – 90o Solution: Identify and step: • Two ways to calculate: 1.10Products of Vectors • Eq (1.18) using magnitudes of the vectors and Φ. • Eq (1.21) using the components of the two vectors. Execute: 1.Φ = 130.0o – 53.0o = 77.0o Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  44. 2. Find the components of vectors A & B 1.10Products of Vectors Read example 1.11 Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  45. The vector product of is donated by Φ Magnitude of the vector (cross) product of A & B Vector Product: • Also called cross product. 1.10Products of Vectors • Vector product is a vector quantity with direction perpendicular to the plane which contain two vectors A and B and a magnitude equal to AB sinΦ. Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  46. When are parallel or anti-parallel • The vector product of any vector with itself is zero Vector Product: • We measure Φ from vector A toward B 1.10Products of Vectors • Φ from 0o – 180o Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  47. maximum Contrast between the scalar & vector product: Scalar product Vector product 1.10Products of Vectors Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  48. We can rewrite 1.10Products of Vectors Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  49. Components: Ax Ay Az Bx By Bz Cx= AyBz - AzBy 1.10Products of Vectors Cy= AzBx – AxBz (1.27) Cz= AxBy - AyBx Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

  50. Vector has magnitude 6 units and is in direction of the +x axis. Vector has magnitude 4 units and lies in +xy plane, making an angle of 30o with the +x axis (figure below).Find the vector product Example 1.12(Calculating a Vector Product): 1.10Products of Vectors Solution: Identify and step: • Eq (1.22), determine the magnitude and right rule for direction. • Using the components of vectors A & B to find vector C components using Eq (1.27). Dr. Y. Abou-Ali, IUST University Physics, Chapter 1

More Related