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Engineering Physics Mechanical Properties of Matter Ch-1 Units and Dimensional Analysis

Math. & Engineering Phys. Department Mansoura University Faculty of Engineering. Engineering Physics Mechanical Properties of Matter Ch-1 Units and Dimensional Analysis. Dr. Mohamed Farhat Othman. Units of Measurement. What is your response if I told you that: I weigh 802.

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Engineering Physics Mechanical Properties of Matter Ch-1 Units and Dimensional Analysis

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  1. Math. & Engineering Phys. Department Mansoura University Faculty of Engineering Engineering PhysicsMechanical Properties of MatterCh-1 Units and Dimensional Analysis Dr. Mohamed Farhat Othman

  2. Units of Measurement What is your response if I told you that: I weigh 802 In any measurement magnitude (the number) as well as the unit (meaning) must be stated. Otherwise, it is meaningless!

  3. Number vs. Quantity • Quantity = number + unit UNITS MATTER!!

  4. Units • Units are very important: • 1- To compare measurements • 2- To distinguish between different physical quantities

  5. Units • Base Units • Ex: Units of Mass, Length, Time • Mass  kg • Length m • Time  sec

  6. M V D = Derived Units • Combination of base units. • Volume (m3 or cm3) • length  length  length 1cm3=1mL • Density (kg/m3 or g/cm3) • mass per volume

  7. SI Units Symbol Quantity Base Unit Abbrev. Length l meter m Mass m kilogram kg Time t second s Temp T kelvin K

  8. Systems of Units

  9. Prefixes In addition to MKS units, standard prefixes can be used, e.g., cm, mm, mm, nm

  10. Conversion between system of units • Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

  11. Conversion between system of units • Lining up conversion factors: = 1 1 in = 2.54 cm 2.54 cm 2.54 cm 1 = 1 in = 2.54 cm 1 in 1 in

  12. cm in Conversion between system of units The length of a piece of paper is 8.0 cm. Convert the length in terms of inch unit. 1 in = 2.54 cm 8.0 cm 1 in 2.54 cm = 3.2 in

  13. gm/cm3 Kg/m3 Dimensional Analysis The density of water is about 1gm/cm3 what is this unit in SI units? 1000kg m3 (100cm)3 1m3 1kg 1000 gm 1 gm cm3

  14. Express the mass of a proton 1.672*10-27kg in terms of the unified mass unit. B) the mass of a neutron is 1,00867u. What is this in kg? 1u=1.6605402*10-27 kg

  15. A women weights 130 Ib and is 5ft and 9in in tall. Express her weight in Newton’s and in meters. 1 Ib= 4.448 N, 1ft=0.3048m, 1in=2.54cm

  16. How old are you in minutes? • Conversion factors: • 365 days = 1 year • 24 hr = 1 day • 60 min = 1 hr 1 yr = 525 600 min

  17. Dimensional Analysis • Dimensional analysis is a simple technique used to • 1-To check the correctness of the form of the equation. • 2-To derive a relation between the physical quantities but it can't have the values of the constants. • 3-To determine the proper units for some particular terms in an equation.

  18. Dimensional analysis The dimension of: 1- The length : [L] 2- The mass : [M] 3- The time : [T] 4- The temperature : [K]

  19. Dimensional Analysis Checking equations with dimensional analysis:

  20. The period (p) of a simple pendulum is the time for one complete swing. How does (p) depends on mass (m) of the bob, the length (L) of the string, and the acceleration due to gravity (g) ?

  21. The wave length  of a wave depends on the speed (v) of the wave and its frequency (f). Decide which of the following equations is correct:  = v f or  = v/ f  = v a f b

  22. Suppose a sphere of Radius (R) is pulled at constant speed (v) through a fluid viscosity η. The force (F) that is required to pull the sphere through the fluid depends on v, R and η, ( F = (const) v R η ) find the dimensions of η .

  23. Thanks for your attention

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