B-2 Physics Dynamics 1 PDF

Module: B-2 Physics Topic 2.2.3 Dynamics  INTRODUCTION On completion of this topic you should be able to: 2.2.3.1 Describe the following: mass force inertia...

Module: B-2 Physics Topic 2.2.3 Dynamics  INTRODUCTION On completion of this topic you should be able to: 2.2.3.1 Describe the following: mass force inertia work power energy (potential, kinetic and total) resultant force and equilibrium heat efficiency. 2.2.3.2 Describe the following with regard to momentum: momentum and conservation of momentum. impulse. gyroscopic principles. friction, its nature and effects, and the coefficient of friction (rolling resistance). 30-03-2024 Slide No. 2  GRAVITY Every object in the universe exhibits a natural force of attraction on every other object. This is called gravitation. It is this force which holds the planets in their orbits around the sun and which, on earth, gives the property of weight to objects. It is gravity that causes unsupported objects to fall towards the centre of the earth. 30-03-2024 Slide No. 3  GRAVITY Newton’s 2nd Law says the force of gravitational attraction between two objects will produce acceleration. The acceleration due to Earth’s gravity on body released is called ‘g’ = 9.8 m/sec2. The formula F = ma is used, and the force acting on a falling body can be calculated in Newtons when the mass of the body is known. W = mg Newtons 30-03-2024 Slide No. 4  WEIGHT On the moon the acceleration due to gravity is only: 2 9.8 m/sec 6 This is because the moon has 1/6 the mass of the Earth. Therefore: W = 100 x 1.63 = 163 N 30-03-2024 Slide No. 5  MASS AND WEIGHT Mass is the amount of matter contained in a body. This value does not vary. Weight varies according to the gravitational force acting on that body. A person of mass 100 kilograms is said to have a weight of 100 kilograms on Earth. But the same person of mass 100 kilograms will weigh considerably less on the moon. Why? 30-03-2024 Slide No. 6  INERTIA Inertia of an object is what causes it to resist any change in its state of motion or rest. 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. 30-03-2024 Slide No. 7  WORK When a force acts on an object and sets it in motion, work is done. Unless the object moves through a distance, the work done is zero. Work done is found by the formula: W = Fs where F = force, s = distance The unit of work in the SI system is the joule which equals 1 Newton metre (Nm). 30-03-2024 Slide No. 8  WORK 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. WORK = FORCE X DISTANCE 30-03-2024 Slide No. 9  POWER Power is the rate of doing work. P=W t When a person climbs a flight of stairs, they perform the same amount of work whether they walk up or run up. When the person runs up, though, they are working at a faster rate and therefore using more power. 30-03-2024 Slide No. 10  POWER The SI unit of power is the watt. One watt is the power required or generated when one joule of work is done in one second. In the Imperial system of measurement, power is expressed in foot-pounds per second. The horsepower is equivalent to 550 foot- pounds per second. 30-03-2024 Slide No. 11  POWER Because Work = Force x distance Power can be written as Force x distance time but distance divided by time is velocity so Power = Force x Velocity P = Fv Example What is implied if you have a 230 kW motor? The drag (air resistance) of an aircraft is 1500 N. What power is required to fly at 360 km/hr? (Ans. in kW). 30-03-2024 Slide No. 12  ENERGY Energy provides the capacity for work to be done. The SI unit of energy is the joule. One joule of energy can do one joule of work. An important concept when thinking about energy is the law of Conservation of Energy which states: Energy can neither be created nor destroyed. It can only be changed from one form to another. 30-03-2024 Slide No. 13  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. 30-03-2024 Slide No. 14  KINETIC ENERGY Kinetic energy is the energy a body has because of its motion. If a mass is held aloft then released, as it falls the potential energy is converted to kinetic energy. The formula for calculating kinetic energy is: KE = ½ mv2. 30-03-2024 Slide No. 15  TOTAL ENERGY A falling mass has maximum potential energy at highest elevation (PE = mgh). Kinetic energy is zero because the ball has no motion (KE = ½mv2). Once the mass is released and begins PE = 10, KE = 0 falling, the potential energy starts to be converted to kinetic energy. Half way through its fall, the potential energy exactly equals the kinetic energy. Then, at an instant immediately before the mass strikes the floor, the kinetic energy is PE = 5, KE = 5 maximum. It has no distance left to fall, so potential energy is close to zero PE = 0, KE = 10 TOTAL ENERGY REMAINS 10 30-03-2024 Slide No. 16  TOTAL ENERGY The law of conservation of energy states that: ‘Energy cannot be created or destroyed, but merely changed from one form to another’. In accordance with this law, the total energy of an object does not change, but potential energy can be transformed into kinetic energy and vice-versa. Hydro-electric power generation is an important example. 30-03-2024 Slide No. 17  TOTAL ENERGY About 25 Tonnes of ancient plant/animal material is in a litre of petrol. Regardless of how much petrochemical energy remains. It is being used at a higher rate that can never be renewed. Activity: Calculate the height of a tree trunk, 0.5m diameter which would provide approx the same energy as I litre of petrol. Use density of wood as 500 kg/m 3. 30-03-2024 Slide No. 18  FRICTION Sliding or rolling contacts have resistance to motion called friction. Friction between shoes & the ground is necessary to be able to walk & run. Friction between a vehicles clutch plate & pressure plate transferring rotary motion from the engine to the gearbox. Likewise, it is the friction between tyres and the road and between brake rotors and discs that helps slow down a vehicle, including an aircraft. Unwanted friction is minimised with lubricant. 30-03-2024 Slide No. 19  COEFFICIENT OF FRICTION The coefficient of friction refers to the differences in friction between various materials. The higher the coefficient of friction (μ), the greater the resistance between the two surfaces. Steel on steel is 0.09. Rubber tyre on airport runway 0.7 (dry) and 0.5 (wet). Teflon on Teflon 0.04. Lubrication reduces friction. 30-03-2024 Slide No. 20  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 30-03-2024 Slide No. 21  FRICTION The amount of sliding friction can be calculated from the relationship: F = μN Where N is the reaction to the weight of the object from the surface on which it is sliding. From above it can be seen why pulling a box with a slight upward angle is easier that pushing when your force may be slightly down on the box. 30-03-2024 Slide No. 22  COEFFICIENT OF FRICTION L W F = μN but N=W-L So reducing lift as soon as possible will increase friction and allow early braking. 30-03-2024 Slide No. 23  ROLLING RESISTANCE Coefficients of rolling resistance are very small. For example: Rubber tyres on concrete 0.02 Ball bearings 0.001 Rolling one surface over another creates less friction than sliding one surface over another. The coefficient of friction determines how much of an object’s weight contributes to the frictional force. 30-03-2024 Slide No. 24  HEAT All matter consists of atoms or molecules which are in constant motion. The energy of this motion is heat. Heat is a form of energy and other types of energy can be transformed, in accordance with the law of conservation of energy, into heat. For example, the chemical energy of the wood is transformed by combustion into a number of by-products, including heat. The sun is the primary source of energy for all life on earth. 30-03-2024 Slide No. 25  HEAT Heat is also found as a consequence of friction. The heat produced by friction is usually unwanted. Usually, heat produced as a by-product of a process is not ideal because it is a loss of energy. Heat can also be generated by electrical means, for example, toasters, irons and hotplates. 30-03-2024 Slide No. 26  EFFICIENCY Energy can neither be created or destroyed. Therefore, it is impossible to build a perpetual motion machine, a machine which outputs more energy than is put in to it. With a simple machine, the efficiency is a ratio of work output to work input. If 100 joules of work is put into a gear train and the output is 90 joules, the efficiency is said to be: efficiency = W (out) x 100 W (in) = 90 x 100 = efficiency = 90%. 100 30-03-2024 Slide No. 27  EFFICIENCY The efficiency of a more complex machine is a measure of how much useful work is produced per unit of energy put in. It is friction that primarily determines the efficiency of a machine, because the friction between moving parts creates heat, sound and, sometimes, light. All of these are energy losses. Reducing friction is usually accomplished by lubrication or streamlining. 30-03-2024 Slide No. 28  MOMENTUM There are 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. M = mv. Momentum is conserved, so if two masses m1 and m2 collide and stick together then: m1v1 + m2v2 = (m1 +m2)v 30-03-2024 Slide No. 29  MOMENTUM Angular momentum is a measure of the tendency of a rotating body to continue to spin about an axis. A spinning skater can vary her RPM by moving her arms in and out, changing the resistance to her rotation. The angular momentum of the spinning weight means the gyroscope would spin indefinitely about the same axis if it weren’t for friction. 30-03-2024 Slide No. 30  MOMENTUM This is the principle behind Governors, which are device used to maintain an RPM for: pumps propellers etc. 30-03-2024 Slide No. 31  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. Impulse I = Ft (Force multiplied by time). 30-03-2024 Slide No. 32  A SIMPLE GYROSCOPE A gyroscope is a rotating mass (rotor) mounted on gimbals, so that its supporting platform or case can be turned in one or more planes around the rotor without changing the rotor’s plane of rotation. Like all rotating masses, the gyroscope has two fundamental characteristics. These are gyroscopic inertia (rigidity in space) and precession. 30-03-2024 Slide No. 33  GYROSCOPIC RIGIDITY Gyroscopic rigidity is the natural property of any rotating mass to resist changes to its plane of rotation. The rotor remains in the same plane of rotation when spinning even if the frame is tilted. This can be used to display aircraft attitude. 30-03-2024 Slide No. 34  GYROSCOPIC PRECESSION Precession is the change of the plane of rotation caused by an external force. If a force is applied to the rotating mass, its plane of rotation will deflect 90° in the direction of rotation. This is called precession. For example, when an aircraft pitches nose down, the precession is This can be used to display the rate experienced as a swing (yaw) left. at which the aircraft is turning. 30-03-2024 Slide No. 35  CONCLUSION Now that you have completed this topic, you should be able to: 2.2.3.1 Describe the following: mass force inertia work power energy (potential, kinetic and total) resultant force and equilibrium heat efficiency. 2.2.3.2 Describe the following with regard to momentum: momentum and conservation of momentum. impulse. gyroscopic principles. friction, its nature and effects, and the coefficient of friction (rolling resistance). 30-03-2024 Slide No. 36  This concludes: Module: B-2 Physics Topic 2.2.3 Dynamics