B-2 Physics Statics Module (PDF)

Module: B-2 Physics Topic 2.2.1 Statics  INTRODUCTION On completion of this topic you should be able to: 2.2.1.1 Describe forces, moments and couples and represent the interaction of these as a vector descri...

Module: B-2 Physics Topic 2.2.1 Statics  INTRODUCTION On completion of this topic you should be able to: 2.2.1.1 Describe forces, moments and couples and represent the interaction of these as a vector describing simple machines and mechanical advantage. 2.2.1.2 Describe the centre-of-gravity of a mass. 2.2.1.3 Describe the elements of theory of stress, strain and elasticity to the following: Tension Compression Shear Torsion 2.2.1.4 Describe the nature and properties of solids, fluids, and gases. 2.2.1.5 Describe the action of pressure and buoyancy in liquids (barometers). 30-03-2024 Slide No. 2  FORCE A force can be described as that which can produce a change in a body’s state of motion. An application of force will: start stop accelerate, or decelerate a mass. If energy is available, then forces can be used to do work. 30-03-2024 Slide No. 3  VECTORS Force is an example of a vector quantity. Vectors need magnitude (size) and direction to be fully defined. Most quantities are scalars and are defined with size only. For example, temperature, length, and time. Scale drawings are a convenient way to represent vectors. 30-03-2024 Slide No. 4  VECTOR ADDITION To add vectors, move one vector’s tail to the other vectors head. (Do not change either vector’s magnitude or direction!) Complete the triangle with the resultant vector. Notice the head of the resultant meets the “free” head of the vector you wish to add. 30-03-2024 Slide No. 5  RESOLUTION OF A VECTOR The 60 N tension force in the chain may be resolved into two components, one horizontal and the other vertical using the standard trig ratios. 30-03-2024 Slide No. 6  RESULTANT FORCE AND EQUILIBRIUM A Sometimes, forces act at different directions on a body. In cases such as these, forces must be resolved to calculate a resultant B net force. B When an object does not change its state of motion or rest, the resultant of all the forces acting on it is zero, and it is said to be in a state of equilibrium. 30-03-2024 Slide No. 7  RESULTANT FORCE AND EQUILIBRIUM For example, if a car is being pushed at one end by a person and opposed at the other end by a similar force, the resultant is the car does not move. These scales are balanced but not in equilibrium. Why? 30-03-2024 Slide No. 8  MOMENTS LOAD MOMENT (load x load arm) EFFORT MOMENT Load Effort arm arm (force x effort arm) Either side of the lever has a moment which is the force multiplied by the distance, called the arm from the fulcrum. The system is balanced when the load moment and the effort moment are equal. The smaller effort force moves through a larger arc to raise the heavier load a small distance. 30-03-2024 Slide No. 9  LEVERS A lever is an example of a simple machine. A simple machine is a device which provides a mechanical advantage (MA). LL EE The purpose of a lever is to perform work  for a load (L) to be lifted FF  by an effort (E) First-class lever  pivoting around a fulcrum (F) e.g. see-saw If the load moved is greater than the effort used, the machine has a positive MA. Second-class lever e.g. Third-class lever wheelbarrow e.g. ice tongs 30-03-2024 Slide No. 10  FIRST CLASS LEVER An example of a first-class lever is a crowbar. EE LL FF The fulcrum is situated between the load and the effort. The load is greater than the effort. MA = Load Effort The lid only needs to be raised a short distance but your hand travels a larger distance. Hence the term “leverage” 30-03-2024 Slide No. 11  FIRST CLASS LEVER EE LL FF If L is 100 kg and E is 10, What is MA ? 10 MA = L The ratio of the distance moved by each end of the E lever will also equal 10. Distance Ratio = MA 30-03-2024 Slide No. 12  MECHANICAL ADVANTAGE The mechanical advantage of a first-class lever depends on the distance moved by effort compared to load. In this example, the lifting arm is 7 times the length of the load arm, therefore the load can be lifted with 7 times less effort. 30-03-2024 Slide No. 13  SECOND-CLASS LEVER An example of a second-class lever could be a cockpit control lever such as a throttle or thrust lever, engine start lever or a flight control lock lever. EE LL FF The load is situated between the fulcrum and the effort. The load is greater than the effort. Positive MA. 30-03-2024 Slide No. 14  MECHANICAL ADVANTAGE A wheel barrow is a second-class lever. In this example, the total arm length is 4 times the length of the load arm. Therefore the effort required is 4 times less. 50 pounds of effort is required to lift 200 pounds of resistance. Both these equal MA. 30-03-2024 Slide No. 15  THIRD-CLASS LEVER An example of a third-class lever is the retraction mechanism on an aircraft landing gear. FF LL EE 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. 30-03-2024 Slide No. 16  MECHANICAL ADVANTAGE In this example, a greater effort is required to lift the load (1600 pounds to move a load of 200 pounds). But the load is moved a far greater distance than the effort applied (8:1). This advantage can be useful in aviation where space for components such as landing gear retraction mechanism is limited. 30-03-2024 Slide No. 17  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 be pulling the rope through 4 times as fast as the load is being raised. The velocity ratio is 4:1 MA = Distance Ratio = VR 30-03-2024 Slide No. 18  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 around an axis. The forces produce a ‘torque’ or twisting force to the aircraft, causing it to roll. 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 30-03-2024 Slide No. 19  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 – geometric centre of the bodies. 30-03-2024 Slide No. 20  CENTRE OF GRAVITY If an irregularly shaped solid is hung first from one point, and then from another point, then its CG is the intersection of verticals passing through these points. Any object that is freely suspended from one point takes up a position that puts its centre of gravity in the vertical passing down from the point of suspension. 30-03-2024 Slide No. 21  CENTRE OF GRAVITY The entire weight of a body is considered to act down through the vertical passing through its CG. The body can be raised without toppling by an upward-acting force applied to the underside of the body directly below the CG. Therefore sling or lift loads as near to the CG as possible. 30-03-2024 Slide No. 22  CENTRE OF GRAVITY CG of an aircraft shifts if passengers, baggage, or equipment in the cabin move, or if unequal amounts of fuel are used from tanks in opposite wings. 30-03-2024 Slide No. 23  CENTRE OF GRAVITY There is a range of acceptable CG positions between a forward limit and an aft limit. 30-03-2024 Slide No. 24  CENTRE OF GRAVITY There is a range of acceptable CG positions between a forward limit and an aft limit. 30-03-2024 Slide No. 25  CENTRE OF GRAVITY There is a range of acceptable CG positions between a forward limit and an aft limit. This will ensure the aircraft remains controllable without becoming tail heavy or nose heavy. 30-03-2024 Slide No. 26  BALANCE OF ROTATING OBJECTS Perfectly circular disc of constant thickness & density with an axle through its centre – disc is balanced at all positions to which it may be rotated around its CG at the centre of the axle. Balance retained regardless of the number of weights added to the disc, providing they are paired off diametrically with equal & opposite moments. 30-03-2024 Slide No. 27  BALANCE OF ROTATING COMPONENTS Even with an object of regular shape – disc or wheel – thickness or other dimensions may vary slightly from manufacture, or because of wear or damage during use. Density may not be perfectly uniform throughout the material. CG may not coincide with the geometric centre or axis of rotation. 30-03-2024 Slide No. 28  BALANCE OF ROTATING COMPONENTS The unbalanced condition will cause vibration during rotation. To rectify problem – CG must be shifted to coincide with centre of rotation. Often done by adding small masses of material to the light side, or by removing small masses of material from its heavy side until it balances. 30-03-2024 Slide No. 29  BALANCE OF ROTATING COMPONENTS Propeller’s supporting mandrel or spindle rolls freely on a pair of horizontal knife edges with very little friction – mass balancing. Heaviest blade moves downward – when perfectly balanced propeller remains stationary in any position to which it is turned – even slight air movements may cause incorrect indication of imbalance. Many other rotating components are balanced during manufacture: landing-gear wheel assemblies helicopter rotors compressors turbines fans rotors in:  generators  magnetos For a component spinning at very high speed even a  gyroscopes tiny amount of unbalance may produce excessive 30-03-2024 vibration Slide No. 30  STRESS / STRAIN / ELASTICITY Stress is the external force acting on an object per unit cross sectional area. Stress = F / A Strain is a measure of the degree of deformation of the material as a result of stress. Strain = (Extension / Original size) X 100% 30-03-2024 Slide No. 31  STRESS / STRAIN / ELASTICITY The elasticity of the material will allow it to return to its natural length, if the strain is less than the material’s elastic limit. Strain below the elastic limit is directly proportional to the applied stress. (This is Hooke’s Law). Doubling the stress doubles the strain. 30-03-2024 Slide No. 32  TENSION Tension stress results from forces tending to pull an object apart. Ropes and cables can support tension. 30-03-2024 Slide No. 33  COMPRESSION Compression is the resistance to external forces trying to push an object together. The weight of an aircraft causes compressive stress to the runway. 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. 30-03-2024 Slide No. 34  SHEAR STRESS 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. Shear stress also occurs in fluids, for example a layer of oil or grease between two sliding metal surfaces, providing lubrication. 30-03-2024 Slide No. 35  TENSION AND COMPRESSION 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. 30-03-2024 Slide No. 36  TENSION AND COMPRESSION In flight – under the influence of aerodynamic loads. On the ground – under the influence of gravity. 30-03-2024 Slide No. 37  TORSIONAL STRESS Torsion or torque will cause 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. 30-03-2024 Slide No. 38  RESIDUAL 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. Can be beneficial. The controlled crazing of some car windscreens in a crash or when hit by a stone is achieved by building residual stress into the glass when the windscreen is made. Also called “Locked In Stress”. 30-03-2024 Slide No. 39  FATIGUE During operation, moving parts experience a variety of loadings, caused by vibration, changes of load, and temperature changes. Repeated applications of small loads may eventually result in fatigue failure. A crack can originate at the point of highest tensile stress in the part. Such a crack can grow progressively and the part’s strength is reduced so much that it suddenly breaks. Fatigue failures are quite common in aircraft and motor cars, and are at least as common as overload failures. 30-03-2024 Slide No. 40  FATIGUE Surface damage like nicks, cuts, scratches, gouges, cracks, or corrosion pits can cause a fatigue failure at that point. These so called ‘stress raisers’ also occur where a part has an abrupt change in shape or section thickness. For this reason sharp edges should be avoided. Flaws beneath the surface of materials are also stress raisers. Typically they are formed within the material when manufactured, or later by improper shaping or heat-treatment techniques. Fatigue failures happen chiefly with metals. 30-03-2024 Slide No. 41  BUOYANCY AND PRESSURE IN LIQUIDS 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. 30-03-2024 Slide No. 42  PRESSURE IN SOLIDS Pressure is defined as: Force per unit area Pressure = Force N/m2 Area Using g = 10 m/s per s Block A, P = 100 x 10 = 250 N/m2 4 Block B, P = 100 x 10 = 1000 N/m2 1 30-03-2024 Slide No. 43  PRESSURE IN GASES When a substance is heated, its molecules move around more rapidly as their thermal energy increases. There is a direct relationship between the temperature of a substance and the motion energy of its molecules. Gas pressure is the net result of the continual bombardment on the walls of the container. 30-03-2024 Slide No. 44  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 fluid in an open container is determined by the: vertical height of the column gravity density of the fluid The pressure is not affected by the volume of the liquid. 30-03-2024 Slide No. 45  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. When the density of other solids or liquids are compared to water, a table of comparative densities or specific gravities can be determined. Gasoline has a specific gravity of 0.72, which means its weight is 72% that of the same amount of water. 30-03-2024 Slide No. 46  DENSITY AND SPECIFIC GRAVITY Lower density materials float on higher density materials. For example gasoline or oil will float on water ice will float on water lead will float on mercury but sink in water A SG of a gas is obtained by comparing its density to that of air. 30-03-2024 Slide No. 47  REFUELLING The SG of aviation fuel varies due to a variety of factors such as: the refining process storage facilities ambient conditions The refueller or engineer must check the SG of the fuel supply, to calculate how many litres will provide the weight of fuel requested: Weight of fuel (kg) = Volume (litres) x SG Do fuel exercise 30-03-2024 Slide No. 48  ARCHIMEDES’ PRINCIPLE Archimedes’ Principle states: An object is submerged in a fluid displaces a volume of fluid equal to its own volume. 30-03-2024 Slide No. 49  ARCHIMEDES’ PRINCIPLE The pressure on the bottom of the object is greater than on the top because it is deeper in the fluid. This creates an upthrust on the object. This upthrust is a force equal to the weight of the fluid displaced – this is the ‘buoyancy force’. Therefore if a body displaces more fluid than its own weight, it will float. 30-03-2024 Slide No. 50  BUOYANCY Hydrometers use Archimedes’ principle to measure the relative density or specific gravity (SG) of liquids. Density of the liquid determines how high or low the float rides in the liquid – the higher the density of liquid, the higher the float rides. A calibrated scale on the float gives a direct reading of the liquid’s SG – read the scale at the surface of the liquid. For example to measure the SG of fuel – hydrometer calibrated to measure SG of ≈ 0.7 for Avgas, & 0.8 for Jet A-1 – SG varies with temperature. 30-03-2024 Slide No. 51  BUOYANCY Three bodies of the same volume but of different SG are shown either floating or submerged in water: Body A with SG of 0.25 – only ¼ submerged Body B with SG of 0.5 – only ½ submerged Body C with SG of 2 – will not float in water – weight is ½’d though If the tank was filled with fluid with SG greater than 2 – Body A & B would float higher & Body C would also float – ships float higher in salt water than in fresh. 30-03-2024 Slide No. 52  PASCAL’S LAW When pressure is applied to a confined liquid, the changes in pressure are transmitted undiminished to all parts of the fluid and its containers. 30-03-2024 Slide No. 53  PASCAL’S LAW Pascal’s Law can be used to provide Mechanical Advantage, e.g. A Hydraulic Jack The same volume of fluid is displaced at each end of the system. 1 psi spread over 10 square inches can support 10 lb so, MA = 10. Note that the large piston will only move up 1/10 of the distance the small piston moves in. 30-03-2024 Slide No. 54  DIFFERENTIAL AREA The same pressure provides different forces according to direction of travel due to the differing area available. This will also affect the speed at which the operation will occur. 30-03-2024 Slide No. 55  ATMOSPHERIC PRESSURE Atmospheric pressure at a location then depends on the weight of the column of air above that location. 30-03-2024 Slide No. 56  ABSOLUTE PRESSURE vs. GAUGE PRESSURE Gauge pressure reads pressure above (or below) atmospheric. Absolute Pressure is Gauge Pressure plus Atmospheric Pressure. The left side of this instrument reads Absolute Pressure. Tyre pressure gauges read Gauge Pressure. 30-03-2024 Slide No. 57  DIFFERENTIAL PRESSURE For passenger comfort, modern aircraft retain a cabin altitude equivalent to 8000’ or 11 psi. Cruising at 29,000 ft, the outside pressure is 4.4 psi. Therefore, the structure of the aircraft is experiencing a differential pressure of 11 - 4.4 = 6.6.psi. This is a significant component of the total stress on the airframe. 30-03-2024 Slide No. 58  SOLIDS Solids have a definite shape and 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). 30-03-2024 Slide No. 59  FLUIDS 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. 30-03-2024 Slide No. 60  GASES Although liquids and gases both share the common characteristics of fluids, they have distinctive qualities of their own. A liquid is regarded as incompressible, 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. 30-03-2024 Slide No. 61  CONCLUSION Now that you have completed this topic, you should be able to: 2.2.1.1 Describe forces, moments and couples and represent the interaction of these as a vector describing simple machines and mechanical advantage. 2.2.1.2 Describe the centre-of-gravity of a mass. 2.2.1.3 Describe the elements of theory of stress, strain and elasticity to the following: tension compression shear torsion 2.2.1.4 Describe the nature and properties of solids, fluids, and gases. 2.2.1.5 Describe the action of pressure and buoyancy in liquids (barometers). 30-03-2024 Slide No. 62  This concludes: Module: B-2 Physics Topic 2.2.1 Statics