Elementary Physics Notes 20OCT PDF

# Elementary Physics ## Units and Dimensions ### Mass Mass is the measure of the amount of matter contained in a body. It is measured in kg (in Standard International or SI unit). Mass can neither be created, nor destroyed, but converted to another form of energy. It, therefore, remains constant....

# Elementary Physics ## Units and Dimensions ### Mass Mass is the measure of the amount of matter contained in a body. It is measured in kg (in Standard International or SI unit). Mass can neither be created, nor destroyed, but converted to another form of energy. It, therefore, remains constant. It is different than the term weight of a body that we are used to, which is explained below later. ### Length Length is the linear dimension of a body or distance between two points and is measured in meters (SI unit). Other non-SI terms are feet, inches, cm, etc. ### Time The standard unit of time is a second (SI unit). Minutes and hours are multiples of the basic unit second. ### Distance For the purpose of navigation on the earth, the distance between two points on the surface of the earth are measured in nautical miles. In aviation, nm is accepted as a common standard unit, though Statute Mile and kilometers are also used in different countries. All three are compared below:- 1. Nautical Mile. One nm is the arc distance on the surface of the earth, which makes one-minute angle at the centre of the earth. 2. Statute Mile. It was an arbitrary distance laid down, and is still in use in UK and USA. 3. Kilometer. It is another way of measuring the distance. One km is the 1/10, 000 part of the distance between equator and the pole along the meridian on the earth. It is equal to 1000 meters. 1 NM = 6080 feet 1 SM = 5280 feet 1 KM = 3280 feet **Mutual conversion between NM, SM, KM** 1 NM = 1.15 SM 1 SM = 1.6 KM 1 NM = 1.85 KM ### Height Height is the vertical distance of any object above a given datum or reference. Meter is the standard unit to measure any length, including height, in physics. But in aviation, in most of the countries, feet is still being used as an acceptable unit for vertical measurement. Russia, France, China are using meters. Therefore, as a pilot, it is important to be able to convert feet into meters and vice versa. 1 meter = 3.28 feet 1 foot = 0.3048 meters **Some of the old FPS unit conversion:** 12 inch = 1 foot 3 feet = 1 yard 1760 yards = 1 statute mile ## Area Area of regular shapes can be found out by mathematical formulae. Area is measured in square meters in SI units (or square inches, square miles, etc, can be square of any length dimensions in other units). Area is a two-dimensional measure such as floor area of a room or a plot of land. Area of some of the regular shapes is given below: - | Shape | Area | Units | | ------------------ | -------------------------- | ------ | | Rectangle | Length x breadth | Sq m | | Square | Side x Side; = square of side | Sq m | | Circle | ΠR²; where Π=22/7 and R is radius | Sq m | | Right angle Triangle | 1/2 x base x height | Sq m | ## Volume Volume of any solid three-dimensional object, such as a box or a room or a tank, is a measure of its capacity. It is measured in cubic meters in SI units. Volume of a rectangular box equals to length x breadth x height. Since length x breadth also equals to area of its floor, volume is also equal to floor area x height. There are different formulae to calculate volume of other different solid shapes such as a sphere, cone, etc. Volume = Length x Breadth x Height Cu m Volume = Floor Area x Height Cu m In aviation, different countries use different units while measuring the volume of the liquids (fuel and oils). UK still used Imperial Gallon, USA has US gallons (different from Imp Gals) and Europe uses Litres. 1 Litre = 1000 cubic centimeters 1 Imp Gallons = 4.546 Litres 1 US Gallon = 3.785 Liters 1 Imp Gallon = 1.2 US Gallon ## Scalar Quantity Those quantities, which have only a magnitude, are termed as scalar quantities. Scalar quantities do not have any direction. Mass, weight, length, pressure, etc., are scalar quantities. ## Vector Quantity Those quantities, which have the magnitude as well as direction of the magnitude, are termed as vector quantities. Wind Velocity is a vector quantity since it has magnitude (speed) as well as direction along which it is blowing. ## Speed Speed is rate of change of displacement (or distance) of any object. Meters per second is the SI unit for speed. Speed is a scalar quantity since it does not have a direction, where as velocity is a vector quantity. Speed = Distance/Time m/s In aviation, most of the aircraft use Knots (Nautical miles per hour) as unit of speed. ## Velocity Velocity of an object is its rate of change of displacement or distance in a particular direction. Velocity is a vector quantity since it has both speed and direction. Meters per second is the SI unit for velocity. Velocity = Distance/Time m/s In a given direction ## Acceleration Rate of change of velocity is acceleration. It is measures in meters per second square in SI units. It is synonymous to the "pick-up" that we are used to while driving a car. A good pick-up means that the acceleration is greater. Acceleration = Velocity/Time m/s² In a given direction ## Gravity All planets attract other planets and objects towards its centre. This force of attraction is termed as gravity. The earth attracts all objects towards its centre due to earth's gravity. Force of gravity between any two heavenly bodies is proportional to the mass of two bodies and inversely proportional to the square of the distance between them (Newton's Law of gravitation). ### Acceleration due to (planet) Earth A freely falling object will accelerate towards the centre of a planet due to its gravity (which depends basically on its mass). On earth's surface, the acceleration due to gravity is 9.81 m/s². Acceleration due to gravity (g) = 9.81 m/s² Towards the centre of the earth ## Three Equations for Linear Acceleration | Variable | Definition | Units | | -------- | --------------------------------------------------------------------------- | -------- | | u | Initial velocity at the beginning of acceleration (zero or any positive value) | m/s | | v | Final Velocity at the end of acceleration | m/s | | a | Acceleration | m/s/s | | t | Time for acceleration acting | s | | s | Distance covered during acceleration | m | Then three important equations relating these quantities are as follows: V = u + at S = ut + 1/2 at² V² = u² + 2 as ## Force Force is an external influence, which changes or tends to change the state of rest or the state of uniform motion of an object. The unit of force in SI units is Newton. It is a vector quantity having a magnitude and a direction. Force = Mass x acceleration Newton Towards the direction of acceleration One Newton is a force that will impart an acceleration of one meter per Second per second to a mass of one kg. ## Weight When you stand on a weighing scale, you get your weight (on earth!!). The weighing scale offers a reaction, which is equal and opposite (in direction) to the force due to gravity, which is pulling us towards the centre of the earth. Thus, when you are stationary on the scale, the weight equals to the force due to gravity, which equals to mass x acceleration due to gravity. The unit of weight is Newton in SI units. We wrongly use the term kg for the weight. Weight = Mass x g Newton Always acting towards the centre of the earth Your weight if taken on moon will be one sixth since the moon's gravity is almost one sixth that of the earth's gravity. ## Centre of Gravity (CG) The Centre of Gravity (CG) of a body or an object is point where the entire weight of a body or an object acts or appears to act. The weight vector, therefore, is always placed at the CG of an aeroplane. When in flight or in space, all the moments take place about the CG of the body. For a ring like object, the CG lies outside the object. For a rotating mass at high speed, such as the car wheels, the CG of the wheel must lie at the axis of rotation for least vibrations. This is the reason that we carry out the "balancing” of the wheels. ## Work Done When a force is acting on a body, and it is displaced from its original position, some work is done. Its units are Joule (J) in SI. Work Done = Force x distance Joules (J) One Joule (J) is the work done when a force of 1 Newton moves the object through 1 metre. ## Energy Energy of a body is its capacity to do work. Therefore, it equals to the work done (earlier) on that body. Unit of energy is Joule (J) which is same as that for the work done (Nm). 1 Joule (j) = 1 Newton x 1 metre Work done = Energy (mutually interchangeable) Energy can neither be created nor destroyed. It can only be converted from one form to another. An object may possess energy due to its height or motion or temperature or pressure, which can be converted to do some useful work. Similarly, if a work is done on a body by lifting it to a greater height, it is then stored in that body as its potential energy; which could be converted back to work. Following are some of the energy types that a pilot should be aware of: 1. **Potential Energy**. An object possesses potential energy by virtue of its height. Potential energy is directly proportional to the mass, gravity and the height of the object. Water stored at height possesses potential energy, which could be converted to mechanical energy through a turbine being rotated by the falling water. Potential energy of an aircraft flying at height could be converted into speed. Potential Energy = Mass x g x height Joule (J) 2. **Kinetic Energy**. An object possesses kinetic energy by virtue of its velocity. Kinetic energy is directly proportional to the mass and square of the velocity. An aircraft flying at high speed (high KE) can zoom up and convert its speed into height. Kinetic Energy = 1/2 x Mass x Velocity² Joule (J) 3. **Pressure Energy**. Fluids possess pressure energy by virtue of its being kept under pressure in a confined space. Pressure energy is directly proportional to the pressure and volume of the fluid. An accumulator storing hydraulic fluid under high pressure is capable of doing some useful work of lowering undercarriage in an emergency. Pressure Energy = Pressure x Volume Joule (J) 4. **Heat Energy**. An object possesses heat energy by virtue of its temperature. Heat energy is directly proportional to the mass and temperature of the object. Heat energy in an engine is converted to the mechanical energy. ## Power Power is rate of doing work. Watt is the unit for power (SI). One watt of power is when one Joule of work is done in one second. Power = Work Done/Time Watt (W) The earlier unit of power still carrying on is the Horse Power and one HP is equal to 33,000 lb-ft of work done per minute (or 550 pound-feet per second). FPS units are not used now. 1 HP = 748 Watts (Conversion factor)