1 / 37

Introduction

Introduction. Aug. 29, 2013 כ"ג אלול תשע"ג. The metric system Length. The metric system Mass. The metric system Time. Units. SI Units – 3 base units: meter (m) as the unit of length kilogram (kg) as the unit of mass second (sec) as the unit of time

tambre
Download Presentation

Introduction

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 Aug. 29, 2013 כ"ג אלול תשע"ג

  2. The metric systemLength

  3. The metric systemMass

  4. The metric systemTime

  5. Units • SI Units – 3 base units: meter (m) as the unit of lengthkilogram (kg) as the unit of masssecond (sec) as the unit of time • CGS – centimeter (cm), gram (gr), second (sec) • BE (British Engineering) – foot (ft), slug (sl), second (sec)

  6. Units – Meter • 1 meter was defined 4 times by different means base on available technology • Current definition: (Oct, 14th 1960)The length of 1,650,763.73 wave-lenghts coming from Isotope Kripton-86 Red-Orange emission.

  7. Units – Kilogram Definition of 1 kilogram

  8. Units – Second • Several definitions that were changed due to inaccuracy and technology advances • Current definition: The time needed for 9,192,631,770 waves cycles of Cesium-133 to occur in an Atomic clock. How do you tell the time in Italy?

  9. Units – cont. • Derived units – units used to define a physical property which are made from the base units, e.g. velocity is defined by length and time. • Large or small quantities of units are presented as multiples of 10.

  10. Conversion of units 829.8 meters The tallest building in the world today is in Dubai. In China they plan on a taller building that will be 2700 ft high Will it really be higher than the BurjKhalifa?

  11. Example 1 Which is higher, 829.8 meter or 2700 ft? 1 ft = 0.3048 m (cover of book) 1 = 0.3048 m/ft 2700 ft * 1 = 2700 ft * 0.3048 m/ft = 822.96 m Not higher!!!

  12. Example 2 – Derived units • The speed limit in the USA is 65 Mph (or Miles/hour). In Israel it is 27.78 m/sec. Where can we drive faster? • Solution A:Convert miles to meters, and hours to seconds • Solution B:Use conversion factor 1 for speed

  13. Solution A 1 mile = 1.609 km = 1609 m 1 = 1609 m/mile 1 hour = 3600 sec 1 = 3600 sec/hour 65 Mph*1/1 = 65miles/hour*(1609m/miles) (3600 sec/hour) = 29.05 m/sec > 27.78 m/sec In the USA we drive faster!!!

  14. Solution B 1 mile/hour = 0.4470 m/sec (book cover) 1 = 0.4470 (m/sec) (mile/hour) 65 mile/hour * 1 = 65 mile/hour * 0.4470 (m/sec) = (mile/hour) = 29.05 m/sec

  15. Units – summary challenge We are defining a new physical dimension called Force. The dimension of force equals to the multiplication of the body mass with the body acceleration (change in speed during a fix time period). Denote the force with the letter F • What are the force dimensions? • What are the force units (in SI units)?

  16. Units – summary challenge 3. A force that is applied on a body having a mass of 1kg cause acceleration of 1 m/sec2, is defined as having magnitude of 1N (Newton).What will be the force applied on a body having a mass of 2kg that will cause acceleration of 5 m/sec2?

  17. Linear Function Y = AX + B or F(X) = AX + B A – the function slope B – the Y value of the function were it crosses the Y axis (X=0)

  18. Graph P1 Y=2X + 4 A = 2 B = 4 P1(X1,Y1) = (0,4) P2(X2,Y2) = (-2,0) A = (Y2-Y1)/(X2-X1)=(0-4)/(-2-0) = 2 P2

  19. Direct and inverse relationships If I manufacture more bikes the total revenue will increase. Direct relationship – if we increase the value of one parameter, the value of the other parameter will be increased as well,and vice versa

  20. Direct and inverse relationships If I smoke more cigarettes per day my life expectancy will be lower Inverse relationship – if we increase the value of one parameter, the other parameter will be decreased, and vice versa

  21. Example 1 Attached PDF -

  22. Trigonometry Mathematical tools to help describe how the physical world works. 3 function:sinus – sin(x)cosinus – cos(x)tangent – tan(x)

  23. Function Definitions Sin(x) = O/H Cos(x) = A/H Tan(x) = O/A O – the length of the side opposite to the angle x A – the length of the side adjacent to the angle x H – the length of the hypotenuse of a right triangle Sin(), Cos() and Tan() are values without units as they are the ratio between lengths.

  24. Additional relations

  25. Example 1 At 10AM the building casts a 50 m long shadow. At 2PM the angle between the sun’s ray and the ground is 300, and it is smaller than the angle of 10AM by 50 Calculate the height of the building and the length of the shadow at 2PM?

  26. Solution H X = 300

  27. Solution – cont. H – the height of the building A1 – the length of shadow at 11AM A2 – the length of the shadow at 2PM X – the angle at 2PM - 300 X+5 – the angle at 11AM Tan(x+5) = H/A1 = H/50 = tan(35) • H = 50 * tan(35) = 35.01 m Tan(x) = H/A2 = tan(30) => A2= H/tan(30) =50*tan(35)/tan(30)= 60.64 m

  28. Calculation of the angle There are cases were we know the lengths of the triangle sides, and need the angle. Each trigonometric function has an inverse function that gives the angle for a given length ratio. X = sin-1(O/H) X = cos-1(A/H) X= tan-1(O/A) The -1 in the exponent does not mean it is a reciprocal. This is the notation.

  29. Example 2 I want to buy a ladder to climb on my house roof for fixing. The height of the roof is 4.5 m. In the store I found a 6m long ladder. On the web I found some tips on working with ladders, suggesting that it must have at least 350 from the ground to maintain stability. Will the ladder from the store maintain its stability?

  30. Solution

  31. Solution O = 4.5 m height of house H = 6 m ladder length* O/H = sin(x) X = sin-1(O/H) = sin-1(4.5/6) = 48.590 The ladder will maintain stability !!! * If the ladder will be put against the roof as shown in the picture we will have to use a shorter length of H in the calculation, and still we will see that the resulting angle will be bigger.

  32. Additional Trigonometric Relations Sinus relation CoSinus relation

  33. Pythagorean Theorem H2 = A2 + O2

  34. Additional Practice Attached PDF

  35. Summary Topics covered: Units and dimensions Unit conversion Linear functions and graph Trigonometry Next meeting: Scalars and vectors

  36. The End

  37. Definition of 1 meter • In 1791 – The French Academy of Science defined it as the distance between the North pole and the equator along the line passing through Paris divided by 10,000,000 • In 1889 – definition as a distance between two marks on a Platinum-Iridium bar kept in a temperature of 0 (zero) degrees Celsius • 1 meter is defined as the distance the light travels in a vacuum in a time of 1/299,792,458 seconds.

More Related