Biophysics Past Paper PDF 2024-2025 (HORUS UNIVERSITY IN EGYPT)

First Level Fall Semester 2024-2025 Biophysics Lab....

First Level Fall Semester 2024-2025 Biophysics Lab. 2 Dimension & units Faculty of Physical Therapy, Level 1, Biophysics, Lab. 2&3 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 :‫الكمية األساسية‬ ‫ هي الكمية التي ال يمكن التعبير عنها بداللة أي كميات أخرى و هناك ثالث كميات أساسية‬ ‫ و تم إضافة أربعة كميات أخرى مثل التيار و شدة اإلضاءة و كمية‬.)‫(الطول و الكتلة و الزمن‬ ‫المادة و درجة الحرارة‬ 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. ‫الكمية المشتقة‬ ‫ هي الكمية التي يمكن التعبير عنها بداللة كميتين أساسيتين أو أكثر مثل (السرعة و العجلة و‬ )‫القوة و الضغط‬ Page 5 Scalar Quantity The quantity that defined only in terms of their magnitude such as price, age, speed, Distance, etc … :‫الكمية القياسية‬ ‫ هي الكمية التي يلزم لتحديدها تحديدا دقيقا معرفة المقدار فقط مثل السعر والسن والسرعة‬.‫والمسافة‬ Page 6 Vector Quantity The quantity that defined not only in terms of their magnitude but also combined with their direction such as force, velocity, displacement, etc … :‫الكمية المتجهة‬.‫ هي الكمية التي يلزم لتحديدها تحديدًا دقيقا معرفة المقدار واالتجاه مثل القوة واإلزاحة‬ 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=𝑚 3 (unit MKS) 3 V = cm × cm × cm = 𝑐𝑚 (unit cgs) Page 13  Quantity Formula Dimension MKS CGS Mass M M Kg gm Basic Length L L Meter cm Time T T Second Second Dimension and units of Basic and Derived Area Volume A=L×L V = L × L× L L2 L3 m2 m3 cm2 cm3 quantities velocity V = x/t LT −1 m. s −1 cm. s −1 Derived Acceleration a = v/t LT −2 m. s −2 cm. s −2 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  Quantity Formula Dimension MKS CGS Energy 1 1) K.E = 2 𝑚V 2 ML2 T −2 Kg. m2. s −2 g. cm2. s −2 (Joule) (erg) 2) P.E = mgh 3) Work = F.d Dimension and units of 5) E = m. C 2 Work W = F.d ML2 T −2 Kg. m2. s −2 g. cm2. s −2 Basic and Derived (Joule) (erg) quantities Derived Power P= E ML2 T−3 Kg. m2. s −3 g. cm2. s −3 T Refractive index c No No unit No unit 𝑛= (n) v dimension Strain (Σ) ∆L No No unit No unit Σ= L dimension Stress F Kg. m−1. s −2 g. cm−1. s −2 σ= ML−1 T −2 A Elastic Modulus σ F/A Kg. 𝑚−1. s −2 g. 𝑐𝑚−1. s −2 E= = Σ ∆L/L ML−1 T −2 (E) Page 15  How to convert certain quantity from measuring system to another 1) Force = mass x Acceleration =m.a Force dimension = 𝑀L𝑇 −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 = 2 𝑚V 2 Energy dimension = ML2 T −2 Energy in MKS = Kg. m2. s−2 (Joule) Energy Units 𝟏𝟎𝟎𝟐 1000 x x 𝟏𝟎𝟕 10000 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 3) Density (ρ) = m/V Density dimension = ML−3 Kg x 1000 g Density Units Density in MKS = 𝑚3 (100) 3 𝑐𝑚3 = Density in cgs (102 )3 106 Kg g = x10−3 𝑚3 𝑐𝑚3 g Kg = x103 𝑐𝑚3 𝑚3 Page 19 Some prefixes of the power of ten Page 20  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 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 + a𝑡 2 = LT −1. T + LT −2. T 2 = [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 𝑚 F = G 12 2 𝑟 𝑀𝑀 MLT −2 = G 𝐿2 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 =G𝑀 G = 𝑴−𝟏 𝑳𝟑 𝑻−𝟐 Page 27  Sheet Check the correctness of the following equations; 𝟏 1) X = 𝑽𝟎 t + 𝟐 a𝒙 2) v = 𝐠𝐱 3) v = 𝐕𝟎 + a𝐱 Define the following terms ◦ Basic quantity ◦ Derived Quantity ◦ Scalar Quantity ◦ Vector Quantity Differentiate between Convert ◦ Physical and numeric constants ◦ 10 m/s to Km/h ◦ 7.8 gm/𝒄𝒎𝟑 to kg/𝒎𝟑 ◦ Rate, Grad, and Ratio Page 28  Tick (✔) or (X) and correct the false answers 1 Basic quantity defined as the quantity that cannot be expressed in terms of one or more other quantities. 2 Basic quantity defined as the quantity that expressed in terms of one or more other quantities 3 Length, Mass and Time abbreviated (L,M and T) considered as basic quantities 4 Length, Mass, Time and Velocity considered as basic quantities 5 Derived quantity defined as the quantity that can be expressed in terms of more than one basic Quantity 6 Velocity, acceleration, force, and pressure are examples for the derived quantities. 7 Length, Velocity, acceleration, force, and pressure are examples for the derived quantities. 8 Scalar Quantity is the quantity that defined only in terms of their magnitude such as price, age and speed 9 Vector quantity is the quantity that defined not only in terms of their magnitude but also combined with their direction such as force and pressure. 1 Vector quantity is the quantity that defined only in terms of their direction such as force and pressure 0 11 The equation V = V0 t + at is not correct V is the velocity, 𝑉0 is the initial velocity, a is the acceleration and t is the time. 1 The equation X = V0 t + 2 a2 t 2 at not correct V is the velocity, 𝑉0 is the initial velocity, a is the acceleration, X is 2 the distance and t is the time. Page 29  Choose the correct answer 13 10 m/s when converted to Km/h is equal (a) 360 (b) 36 (c) 0.0000277 (d) 3.6 14 Express 7800 Kg/m3 in CGS system of units (a) 7.8 (b) 7.8 x 106 (c) 780 (d) 0.078 15 1 Newton equivalent to when converted to Dyne multiplied by (a) 105 (b) 10−5 (c) 103 (d) 10−3 16 The dimension of Viscosity is (a) MLT (b) ML−1 T −1 (c) ML2 T −2 (d) ML2 T−1 17 The dimension of Energy is (a) MLT (b) ML−1 T −2 (c) ML2 T −2 (d) ML2 T −1 18 The dimension of Work is (a) MLT (b) ML−1 T −2 (c) ML2 T −2 (d) ML2 T −1 Page 30