Physics Notes PDF

Matter. Matter refers to everything which occupies space, and has mass which exists in one of three physical states, solid, liquid and gaseous. Matter is made up of small particles. Simplest form of matter are elements whose particles are made up of atoms. Atoms are made up of particles protons...

Matter. Matter refers to everything which occupies space, and has mass which exists in one of three physical states, solid, liquid and gaseous. Matter is made up of small particles. Simplest form of matter are elements whose particles are made up of atoms. Atoms are made up of particles protons and neutrons. Four fundamental interactions within an atom: 1. Gravity. This is the same as already discussed, but very insignificant on the atomic scale 2. The Weak Nuclear Interaction, which contributes to radio activity. 3. The Electromagnetic Interaction. Acts between the nucleus and electrons and is the source of electrical and magnetic energy. 4. The Strong Nuclear Interaction. Holds the nuclei together. Pure copper is an element because it is comprised only of pure copper atoms. All atoms follow this rule: Maximum number of electrons possible in each shell = 2n\* N= the shell number Ions Atoms which have lost or gained a electron during a process. An atom losing an electron will become positive An atom gaining an electron will become negative Isotopes Atoms of the same element with a different number on neutrons. Atomic number remains the same but atomic mass changes. Compounds One or more elements combining in such a way to create substances called compounds. This is called chemically bonding and happens when atoms bond together. They share electrons and form molecules. A compound is matter formed by chemically bonding two or more chemical elements. Mixtures Is a mixture of two or more substances where both substances retain their own individual characteristics. Do not combine chemically as they do in a compound. States of Matter All atoms and molecules are in a constant state of vibration. The internal kinetic energy determines its physical state. Internal KE is what we know as heat. Elements, compounds and mixtures exist as solids liquids and gases depending on their internal energy or heat content. The physical state of a compound has no effect on a compound's chemical structure. Solids A solid has definite volume and shape and is independent of it its container. Very little heat energy therefore the molecules and atoms can't move far from their relative position. For this reason, solids are incompressible. Liquids Liquids have definite volume but no shape. Molecular movement increases in liquids. Heat is added to a solid to increase molecular movement to overcome their rigid shape. Still not far enough apart to make compressing possible. In liquid, molecules are still partially bonded known as surface tension. Gas As heat energy is continually added molecular movement continues to increase until the liquid reaches a point where surfaces tension can no longer hold the molecules down. Molecules escape becoming gas or vapour. Gasses are compressible **Statics** A force can produce a change in a body's state of motion. An application of a force will: Start, Stop, Accelerate or decelerate a mass. If energy is available, then forces can be used to do work. When object doesn't change its state of motion the resultant of all the forces acting on it is zero. This is a state of equilibrium. Mechanical Advantage MA = Load/Effort The purpose of a lever is to perform work, for a load (L) to be lifted by an effort (E), pivoting around a fulcrum (F). Fulcrum -- The point in which a leaver is placed to get purchase. An example of a first class lever is a crow bar. A black and white drawing of a scale Description automatically generated with medium confidence The fulcrum (F) is situated between the load (L) and the effort (E), and the load is greater than the effort. Examples of a second-class lever include cockpit control levers, such as a throttle or thrust lever, and a simple wheelbarrow.  The Load is situated between the fulcrum and the effort. The load is greater than the effort. Positive MA An example of a third-class lever is the retraction mechanism on an aircraft landing gear A black and blue arrow on a black line Description automatically generated The effort is between the fulcrum and the load. The effort is greater than the load, and moves through a smaller distance MA is less than 1 Velocity Ratio A Velocity Ratio is the direct ratio of two speeds that may be present in the same system. For example, consider a pulley system that uses an MA of 4. The operator will pull through a metre of rope to raise the load by 0.25m. Therefore, the rope moves 4 times as fast as the load is being raised. The velocity ratio is 4:1 So, MA = Distance Ratio = VR Couples A 'couple' is a type of moment which is derived from two equal forces acting in parallel but opposite directions on two different points of a body. If a control input is made to turn the aircraft to the left, a force is generated at both the left wing tip and the right wing tip through the ailerons. The forces are equal, but act in opposite direction. The forces produce a 'torque' or twisting force to the aircraft, causing it to turn. If the wing span of the aircraft is b metres, then the torque produced by this couple is given by: T = F x b Nm Centre of Gravity The Centre of Gravity ('CG' or 'C of G') of a body is the point from where the weight appears to act, irrespective of the body's position. The cg of regularly shaped bodies of uniform density is easy to find. It is simply the geometric centre of the bodies. If an irregularly shaped solid is hung first from one point, and then from another point, its CG is the intersection of the verticals passing through these points. The body can be raised without toppling by an upward-acting force applied to the underside of the body where the vertical exactly leaves it. Application of the upward force at any other point would tend to tilt the body. Therefore sling or lift loads as near to the CG as possible. STRESS, STRAIN and ELASTICITY Stress is the force acting through a section of solid material and defined as force per unit area. Stress = Force/Area Strain is the deformation of the material as a result of the stress. If the strain is less than the material's elastic limit, the elasticity of the material will allow it to return to its natural length Strain below the elastic limit is directly proportional to the applied stress (Hooke's Law). Doubling the stress will double the strain, (below the elastic limit). Tension describes forces that tend to pull an object apart. Flexible steel cable used in aircraft control systems is an example of a component designed to withstand tension loads. Compression is the resistance to an external force that tries to push an object together. Aircraft riveting is performed using compressive forces. When compression loads are applied to the rivet head, the rivet shank will expand until it fills the hole and forms a butt to hold the materials together Shear stresses occur when external forces distort a body so that adjacent layers of material tend to slide over one another. Shear stress tries to slice a body apart.  An aeroplane wing or a helicopter rotor blade is very similar to a plank or board. Aerodynamic and gravitational forces try to bend the wing or blade upwards and downwards. Consequently, the top and bottom surfaces of the wing are under alternating compression and tensile stresses and must be constructed to withstand the fatigue that could develop from this situation. Repeated applications of small loads may eventually result in fatigue failure. Fatigue failures are quite common in aircraft and motor cars, and are at least as common as overload failures. Tortional Stress Torsion or torque is a form of shear stress. If a twisting force is applied to a rod that is fixed at one end, the twist will try and slide sections of material over each other. The result is that, in the direction of the twist, there is compression stress and in the direction opposite to the twist, tension stress develops. A diagram of stress and tension Description automatically generated Residual Stress ("Locked In Stress") Abrupt or uneven temperature changes tend to cause internal stress. This often occurs when heat-treating metals. This effect often explains why a component fails in service even though its externally applied stress levels are low. PRESSURE and BUOYANCY Both liquids and gases are fluids, therefore the theory behind buoyancy and pressure in liquids, such as water, and gases, such as air, is similar. An important difference to remember, though, is that liquids are considered incompressible, that is, have a constant density, while gases are compressible. Pressure is defined as force per unit area. Pressure = Force/Area Pressure in Fluids **Pressure is still defined as Force per unit area, but in a fluid it is caused by the** **continual bombardment of the molecules against the inside of the container** **The pressure exerted by a column of liquid is determined by the vertical height of the column, gravity, and the density of the fluid.** **Density and Specific Gravity** Density is defined as the mass per unit volume of a substance. A given volume of lead has many times the mass of the same volume of water. Specific gravity is the ratio of the density of a substance to the density of some substance (as pure water) taken as a standard when both densities are obtained by weighing in air Gases are compared to air to obtain an SG (specific gravity). The term Relative Density is use d to compare the density of air at different altitudes to sea level Buoyancy Archimedes principle states that an item placed in fluid will displace a volume of fluid equal to its own volume. If a body displaces more fluid than its own weight it will float. Lower density materials float on higher density materials. For example: 1. gasoline or oil will float on water; Water sinks to the bottom of a petrol tank. 2. ice will float on water; 3. lead will float on mercury but sink in water. Use of Pressure for MA Pascal's law states ,that when pressure is applied to a confined liquid, the liquid exerts an equal pressure at right angles to the container that encloses it  Pascal's Law can be used to provide Mechanical Advantage, e.g. A Hydraulic Jack Measurement of Pressure Atmospheric pressure at a location then depends on the weight of the column of air above that location. Typically 14.7 psi at sea level up to 4.4.psi at 29,000 ft. Gauge pressure reads pressure above (or below) atmospheric so Absolute Pressure is Gauge Pressure plus Atmospheric Pressure. Tyre pressure gauges read Gauge Pressure Properties of Solids, Liquids and Gases Solids have a definite shape and a definite volume which is independent of its container. In a solid the forces (bonds) that keep the atoms or molecules together are strong. Therefore, a solid does not require outside support to maintain its shape. Most metals are solids and as such are usually hard and strong and capable of being shaped mechanically, (malleable and ductile). Both liquids and gases are classified as fluids. At any point on the surface of a submerged object, the force exerted by a fluid is perpendicular to the surface of the object. The force exerted by the fluid on the walls of the container is perpendicular to the walls at all points. Although liquids and gases both share the common characteristics of fluids, they have distinctive qualities of their own. A liquid is regarded as incompressible, (fixed density) whereas a gas is comparatively easy to compress. A change in volume of a gas can easily be achieved by changes of temperature and/or pressure. A given mass of gas has no fixed volume and will expand continuously unless restrained by a containing vessel. Kinetics Kinetics is all about states of motion. Displacement refers to the position of an object relative to its point of origin. This is different to distance which is the total length travelled by an object from its point of origin. Speed and Velocity However, velocity is a vector quantity, so direction is important. Speed is a scalar quantity, so direction is irrelevant. Average speed is distance travelled divided by time taken. Average velocity is the final displacement divided by the total time. Acceleration When an object has an initial velocity then, after a period of time, that velocity has changed (increased or decreased), the object is said to have accelerated. Acceleration can be positive or negative. Negative acceleration is called deceleration. Acceleration is the rate of change in velocity. Acceleration = velocity/time Acceleration is a vector, so a change in direction even when undertaken at constant speed, is an acceleration. NEWTONS LAWS 1. A body will remain at rest or continue its uniform motion in a straight line until acted upon by an external net force. This law is a statement about INERTIA which is the property of mass that resist changes in motion. 2. The acceleration of a body is directly proportional to the force applied to it and is inversely proportional to the mass of the body. This law is represented by F=ma. 3. For every action, there is an equal and opposite reaction. The upward thrust of a rocket is the reaction to the force propelling the mass of hot gas downward. Linear Motion Motion is said to be uniform if equal displacements occur in equal periods of time. In other words constant velocity. Average velocity = displacement/time Average speed = distance/time Circular motion In accordance with Newton's First Law, the object would shoot off on a straight path unless a Centrifugal Force is continually applied to keep it turning along the curve. Centripetal force is given by Newtons 2nd Law F = ma where m is mass, v is velocity, w is angular velocity (rpm) and r is the radius. Therefore doubling the rpm, quadruples the centrifugal force, which in a grinding wheel, for example, is trying to pull it apart! Orbits The Earth orbits the Sun and the Moon orbits the Earth. In both cases the orbiting body uses the centrifugal force created by their motion to balance the attraction of gravity. PERIODIC MOTION Periodic motion or simple harmonic motion refers to repeated motion, i.e. that which repeats over time. E.g A pendulum The energy contained in a body moving with SHM is called wave energy. SHM occurs around an equilibrium position when a mass is subject to a linear restoring force. A linear restoring force is one that gets proportionally larger with displacement from the equilibrium position. A mass on a spring is a good example -- when stretched, it exerts a restoring force which tends to bring it back to its original length. The time that it takes to make one complete repetition or cycle is called the period of the motion. We will usually measure the period in seconds. Frequency is the number of cycles per second that an oscillator goes through. Frequency is measured in \"hertz\" which means cycles per second. Period and frequency are closely connected; they contain the same information: T = 1/f or f = 1/T RESONANCE If two objects have the same natural frequency and are joined to each other, when one of them vibrates, it can transfer its wave energy to the other object making it vibrate. This transfer of energy is known as resonance Because resonance can induce vibration it can exert destructive forces on an aircraft. For example, it is possible to have portions of an aircraft, such as the propeller, vibrate in resonance at certain engine speeds HARMONICS Harmonics exist as multiples of an original, natural frequency. That is, if the natural frequency is 100 Hz: the 1st harmonic is at 200 Hz and the 2nd harmonic is at 300 Hz etc Harmonics can resonate as well as natural frequencies TOPIC 2.3: DYNAMICS Dynamics is the study of forces at work in motion, and the use of energy. Difference between weight and mass Go to the moon, whose mass I/6 that of the Earth, and your weight will not be the same. You will still have 70 kg of mass, but the weight reduces to 70/6 x 9.8 ≈ 114 Newtons Our earthly muscles, used to supporting 700 N, can make our 114 N body jump much higher. Travel to Jupiter, (mass 2½ times Earth) and you will weigh 70 x 9.8 x 2.5 ≈ 1715 N The same muscles will collapse under the stress of trying to support this force. Inertia Inertia is the property of a mass which causes it to resist any change in its state of motion Newton's first law of motion states: A body will remain at rest or continue its uniform motion in a straight line until acted upon by an external net force. The larger the mass, the greater the inertia. Work When a force acts on an object, overcomes inertia, and sets it in motion, work is done. Work done formula is W=Fs F= force S= distance The unit of work in the SI system is the joule, which equals 1 Newton metre (Nm) If an object is moved 10 metres by a force of 100 newtons, the work is calculated as: W = Fs W = 100 x 10 (Nm) W = 1 000 joules. In the Imperial system of measurement, a measure of work is the foot-pound, the effort of raising one pound of mass by one foot. POWER Power is the rate of doing work. If a person climbs a flight of stairs, they perform the same amount of work whether they walk up or run up. However, when the person runs up they are working at a faster rate and therefore using more power. The unit of power is watt In the imperial system of measurement, power is expressed in foot/pounds per second and one horsepower is equivalent to 550 foot/pounds per second and 746 Watts Because Work = Force x distance Power ac be written as Force x distance over time. but distance divided by time is velocity so Power = Force x Velocity P = Fv (N x m/s = Watts) Energy Energy provides the capacity for work to be done and effect change. The SI unit of energy is the joule. One joule of energy can do one joule of work assuming there have been no loses like friction Energy can neither be created nor destroyed. It can only be changed from one form to another. For example, a car turns the chemical energy found in petrol into mechanical energy, heat and sound. Potential Energy The potential energy in a body or of a body means stored energy, stored in the body because of its position, condition or chemical nature. Hydro electric power uses the energy stored by a mass of water flowing downhill. A drum of gasoline, a stick of explosive, or a chocolate bar all contain potential energy, because of their chemical composition.  Kinetic Energy Kinetic energy is energy a body has because of its motion. If a body is held aloft and then released, as it starts to fall to ground the potential energy is converted to kinetic energy. FRICTION Such sliding or rolling contacts have resistance to the force that causes the motion. This resistance is called friction. There are three types of friction 1\. Starting or Static - Overcoming initial resistance until breakaway occurs. 2\. Sliding - Resistance during steady motion. 3\. Rolling - Single point contact resistance is less than sliding. Still need some friction otherwise the wheel will not grip. Rolling one surface over another creates less friction than sliding one surface over another. Heat Heat is one of the most useful forms of energy because of its direct relationship with work, and with the use of engines. Heat is also found as a consequence of friction. The heat produced by friction is usually unwanted. Efficiency With any machinery, the efficiency is the ratio of work output to workor energy input. Friction primarily determines the efficiency of a machine. Friction is reduced by lubrication or streamlining. Momentum Inertia has been defined as the tendency of a mass to resist changes in its state of motion. Momentum however is the product of this inertia and the motion it already has. Two types of momentum: Linear and Angular Linear momentum is a measure of the tendency of a moving body to continue in motion along a straight line. Momentum is defined as the product of the mass and velocity of a body. Angular momentum is a measure of the tendency of a rotating body to continue to spin about an axis. Impulse **If a force is applied to a moving body, that body's state of motion is altered.** **The momentum of the body is changed by an amount called the Impulse.** A spacecraft's "burn" i.e. applying thrust for a number of seconds is an example of an Impulse. Topic 2.4 Fluid Dynamics A liquid is difficult to compress. Often regarded as incompressible A given mass of liquid occupies a given volume in a container. A gas is easy to compress. Changes volume with pressure A gas has no fixed volume, it changes volume to expand to fill its containing -- it will completely fill the vessel, so no free surface is formed Viscosity Some fluids flow more readily, than others, and the term viscosity refers to the 'stiffness' of a fluid and is defined as the resistance of a fluid to flow. Thick oil is more resistant to flow than light sewing machine oil, so is more viscous. Viscosity Index The viscosity index of a fluid is a measure of the change in the viscosity of a fluid with a change in its temperature. For most liquids, viscosity decreases with increasing temperature. For lubricating oils used in aircraft, a low viscosity index is good because this means the properties of the oil will not change much over a wide range of operating temperatures.