Lecture 1, Biophysics, HUE AHST, 2024

BIOPHYSICS FIRST LEVEL 2024-2025 Prepared By Dr. Nermin Ali Dr. Enas Lotfy Lec No. 1 Course Code: FAC-104 Page 1 Dimension and units Page 2  Physical quantities can be clas...

BIOPHYSICS FIRST LEVEL 2024-2025 Prepared By Dr. Nermin Ali Dr. Enas Lotfy Lec No. 1 Course Code: FAC-104 Page 1 Dimension and units Page 2  Physical quantities can be classified in two ways Physical Physical quantities Or quantities Basic Derived Scalar Vector Quantities Quantities Quantities Quantities Page 3  Basic definitions Basic Quantity: Basic quantity is defined as the quantity that cannot be expressed in terms of one or more other quantities. There are three basic quantities namely, Length, Mass and Time abbreviated (L, M, and T). There are other four quantities add including Current, Luminous intensity, mol and temperature Page 4 Derived Quantity Derived quantity is defined as the quantity that can be expressed in terms of more than one basic quantity. Examples of derived quantities are Velocity, acceleration, force, pressure. Scalar Quantity The quantity that defined only in terms of their magnitude such as price, age, speed, etc … Page 5 Vector Quantity The quantity that defined not only in terms of their magnitude but also combined with their direction such as force, velocity, etc … Page 7  Difference between dimension and unit Dimension: Describes the physical nature of a quantity, like length, mass, or time. It indicates the type of measurement without referencing specific units or numerical values. Example: The dimension of length is [L]. Unit: Specifies the standard for measuring a dimension, giving it a numerical value. Example: length can be measured in meters (m) or kilometers (km). In summary dimension defines what is being measured, while unit defines how the measurement is quantified. Page 8 Basic Quantities Page 9 Basic Quantities and their dimensions Name SI Unit Dimension Length Meter (m) [L] Time Second (S) [T] Mass Kilogram [M] Electrical Current Ampere (A) [I] Temperature Kelvin (K) [θ] Amount of substance Mole [N] Luminous intensity Candela (C) [J] Page 10  System of Units F.P.S C.G.S M.K.S Page 11 Page 12  Area and Volume Area of specific shape known as their length multiplied by the width A = L × L = 𝐿2 (Dimension) A = m × m = 𝑚2 (unit MKS) A = cm × cm = 𝑐𝑚2 (unit cgs) Volume of specific shape known as their length multiplied by the width and height V = L × L × L = 𝐿3 (Dimension) V = m × m × m = 𝑚3 (unit MKS) V = cm × cm × cm = 𝑐𝑚3 (unit cgs) Page 13  Quantity Formula Dimensio MKS CGS n Mass M M Kg gm Length L L Meter cm Basic Time T T Second Second Dimension and units of Area A=L×L L2 m2 cm2 Volume V = L × L× L L3 m3 cm3 Basic and Derived quantities velocity V = x/t LT −1 m. s −1 cm. s −1 Acceleration a = v/t LT −2 m. s −2 cm. s −2 Derived Force F=m×a MLT −2 Kg.m. s −2 g.cm. s −2 (Newton) (dyne) Pressure P = F/A ML−1 T −2 Kg. m−1. s −2 g. cm−1. s −2 Viscosity η= F.d ML−1 T −1 Kg. m−1. s −1 g. cm−1. s −1 A.v Density ρ = m/V ML−3 Kg. m−3 g. cm−3 Page 14  How to convert certain quantity from measuring system to another 1) Force = mass x Acceleration =m.a Force dimension = 𝑀𝐿−1 𝑇 −2 Force in MKS = Kg. 𝐦. 𝐬−𝟐 (Newton) Force Units 1000 x 100 x 𝟏𝟎𝟓 Force in cgs = g. 𝐜𝐦. 𝐬−𝟐 (dyne) Newton = 𝟏𝟎𝟓 dyne dyne = 𝟏𝟎−𝟓 Newton Page 16  1 2) Energy = K.E = 𝑚V 2 2 Energy dimension = ML2 T −2 Energy in MKS = 𝐊𝐠. 𝒎𝟐. 𝒔−𝟐 (Joule) 𝟏𝟎𝟎𝟐 Energy Units 1000 x 10000 x 𝟏𝟎𝟕 Energy in cgs = 𝐠. 𝒄𝒎𝟐. 𝒔−𝟐 (erg) Joule = 𝟏𝟎𝟕 erg erg = 𝟏𝟎−𝟕 Joule Page 17 3) Velocity = x/t Velocity dimension = LT −1 𝐊𝒎 x 1000 𝐦 Velocity Units (Velocity in MKS) 𝒉 (60 x 60) 𝒔𝒆𝒄 (Velocity in cgs) 3600 K𝒎 𝐦 = x 1000 ℎ 𝟑𝟔𝟎𝟎 𝑠𝑒𝑐 𝐦 K𝒎 = x 3600 𝑠𝑒𝑐 1000 ℎ Page 18 4) Density (ρ) = m/V Density dimension = ML−3 𝑲𝒈 x 1000 𝒈 Density Units Density in MKS = 𝒄𝒎𝟑 = Density in cgs 𝒎𝟑 (𝟏𝟎𝟎)𝟑 (𝟏𝟎𝟐 )𝟑 Kg 𝟏𝟎𝟔 g = x10−3 𝑚3 𝑐𝑚3 g Kg = x103 𝑐𝑚3 𝑚3 Page 19  Differentiate between ❖ Ratio : Change in quantity relative to the same quantity ❖ Rate : Change in quantity with respect to time Grade ❖ Gradient : Change in quantity with respect to distance Page 21  Ratio ❖ Refractive index (ratio) Quantity Ratio = Same Quantity Refractive index Ratio = Velocity of light in vacuum Velocity of light in 𝒎𝒆𝒅𝒊𝒖𝒎 Refractive index has no dimensions no unit Page 22  Rate Quantity Rate = 𝑻𝒊𝒎𝒆 Velocity Rate change of velocity = 𝑻𝒊𝒎𝒆 𝑳𝑻−𝟏 Dimension of Rate change of velocity = = 𝑳𝑻−𝟐 𝑻 in MKS = m. 𝐬−𝟐 Units of Rate change of velocity in cgs = cm. 𝒔−𝟐 Page 23  Gradient Quantity Gradient = 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 Force Force gradient = 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑴𝑳𝑻−𝟐 Force gradient dimension = = 𝑴𝑻−𝟐 𝑳 in MKS = Kg.𝐬−𝟐 Force gradient Units in cgs = g.𝒔−𝟐 Page 24  Difference between Numeric and Physical Constants ❖ Numeric constants have no dimensions and no units. Examples: Strain and Refractive index. ❖ Physical constants have both dimensions and units. Examples: Speed of light and acceleration due to gravity. Page 25  Dimensional Analysis 1) To check the correctness of mathematical equations that describe physical experiment ‫إلختبار مدى صحة معادلة رياضية تصف تجربة فيزيقية‬ 𝟏 Check the correctness of the equation X = 𝑽𝟎 t + a𝒕𝟐 𝟐 Dimensions of L.H.S. X = [L] 𝟏 Dimensions of R.H.S. 𝑽𝟎 t + a𝒕𝟐 = 𝑳𝑻−𝟏. T + 𝑳𝑻−𝟐. 𝑻𝟐 = [L] + [L] = [L] 𝟐 LHS = RHS Equation may be correct Page 26  2) To check units of certain constant in the equations Find dimension and units of the gravitational constant for masses m1 , m2 separated a distance r; 𝑚 1 𝑚2 F=G 2 𝑟 −𝟐 𝑴𝑴 𝑴𝑳𝑻 =G 𝟐 𝑳 𝑴𝑴 𝑴𝑳𝑻−𝟐 = G Dimension G = 𝑴−𝟏 𝑳𝟑 𝑻−𝟐 𝑳𝟐 Unit in MKS G = 𝑲𝒈−𝟏 𝒎𝟑 𝒔𝒆𝒄−𝟐 𝑴𝑳𝑻−𝟐 𝑳𝟐 = G 𝐌𝐌 Unit in cgs G = 𝒈−𝟏 𝒄𝒎𝟑 𝒔𝒆𝒄−𝟐 𝑻−𝟐 𝑳𝟑 = G 𝐌 G = 𝑴−𝟏 𝑳𝟑 𝑻−𝟐 Page 27  Thank You Course Code: FAC-104 Page 31