B-2 Physics: Kinetics PDF

Module: B-2 Physics Topic 2.2.2: Kinetics  INTRODUCTION On completion of this topic you should be able to: 2.2.2.1 Describe the following aspects of linear movement: uniform motion in a straight line...

Module: B-2 Physics Topic 2.2.2: Kinetics  INTRODUCTION On completion of this topic you should be able to: 2.2.2.1 Describe the following aspects of linear movement: uniform motion in a straight line motion under constant acceleration (motion under gravity). 2.2.2.2 Describe the following aspect of rotational movement: uniform circular motion (centrifugal/centripetal forces). 2.2.2.3 Describe periodic motion and pendular movement. 2.2.2.4 Describe simple theory of the following: vibration harmonics resonance. 2.2.2.5 Describe velocity ratio, mechanical advantage and efficiency. 30-03-2024 Slide No. 2  DISPLACEMENT 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. Displacement takes direction into consideration, but distance does not care about direction. In the picture, the aircraft is travelling a wildly erratic course. The distance it travels will be very different to its displacement. 30-03-2024 Slide No. 3  DISPLACEMENT The aircraft may travel a total distance of, say, 2 km as it veers left and right. It’s displacement, measured only as the linear difference between the start point and finish point, will be less. The displacement of the aircraft in an easterly direction only is even less. 30-03-2024 Slide No. 4  SPEED AND VELOCITY A similar distinction can be made between speed and velocity. They both refer to the distance travelled per unit of time, for example, miles per hour, metres per second etc. 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 total displacement divided by the total time. 30-03-2024 Slide No. 5  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. Average acceleration is found by dividing the change in velocity by the total time taken for this change to occur. A formula can be used to represent this: a =Δv Δt (acceleration equals change in velocity divided by change in time) or, a = (v-u) t where v = final velocity, u = initial velocity and t = time. 30-03-2024 Slide No. 6  LINEAR MOTION 30-03-2024 Slide No. 7  NEWTON’S LAWS of MOTION Newton’s First Law may be stated as: ‘A body will remain at rest or continue its uniform motion in a straight line until acted upon by an external net force’ In the absence of an external force acting on the object, there can be no acceleration. This law is a statement about inertia. Inertia is the property of mass that resists changes in motion. 30-03-2024 Slide No. 8  NEWTON’S LAWS of MOTION Newton’s Second Law of motion states ‘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 the formula: F = ma (force equals mass multiplied by acceleration). When a force acts on an object, giving it motion, it gains momentum. Once an object has momentum, it takes more force to change the motion. 30-03-2024 Slide No. 9  NEWTON’S LAWS of MOTION Newton’s Third Law of motion states: ‘For every action, there is an equal and opposite reaction’ “Equal” means equal in size and “Opposite” means opposite in direction. 30-03-2024 Slide No. 10  CIRCULAR MOTION Tangent to circle A mass travelling in a circle needs a constant force in towards the centre to continuously accelerate it. It’s a change of direction of the velocity vector not the size. However at any instant, if the string breaks, the mass will to fly off on the straight line that forms a tangent to the curve of its path. 30-03-2024 Slide No. 11  CIRCULAR MOTION Tangent to circle Centripetal force is given by Newtons 2nd Law F = ma = mv2 = mω2r r where m is mass, v is velocity, ω is angular velocity (rpm) and r is the radius. 30-03-2024 Slide No. 12  CIRCULAR MOTION When components rotating at high speed and have a large radius and mass, the centrifugal forces will be very high. Such components must be designed with adequate strength to withstand these loads and must be properly balanced to prevent excessive vibration. Grinding wheels can fly apart if allowed to exceed their maximum RPM. 30-03-2024 Slide No. 13  CIRCULAR MOTION Some examples of aircraft components susceptible to centrifugal stresses are: Gas turbine engine turbines and compressors Propellers and helicopter rotor blades Wheels and tyres 30-03-2024 Slide No. 14  CF ORBITAL MOTION V Orbiting bodies use the centrifugal force created by their motion to balance the attraction of gravity. The further from the Earth the craft is, the slower the orbital speed needs to be. At a height of about 22,300 miles, we have a Geosynchronous orbit. W The orbit where the satellite speed matches the rotation of the Earth, and it stays over the same spot. The “weightlessness” experienced by an astronaut is a result of the same equilibrium. Their weight, is balanced by centrifugal force. 30-03-2024 Slide No. 15  PERIODIC MOTION Periodic motion or simple harmonic motion (SHM) refers to repeated motion i.e. that which repeats over time. Waves transmit their energy in SHM. 30-03-2024 Slide No. 16  PERIODIC MOTION SHM occurs around an equilibrium position when a mass is subject to a linear restoring force. A linear restoring force is one that gets progressively larger with displacement from the equilibrium position. 30-03-2024 Slide No. 17  SIMPLE HARMONIC MOTION Elasticity is the property of an object or material which causes it to be restored to its original shape after distortion. It is said to be more elastic if it restores itself more precisely to its original configuration – a piano wire is MORE elastic than a rubber band. A spring is an example of an elastic object – when stretched, it exerts a restoring force which tends to bring it back to its original length – restoring force is generally proportional to the amount of stretch, as described by Hooke's Law. The motion is sinusoidal and demonstrates a single resonant or natural frequency. A mass on a spring has a single resonant frequency. For any given oscillator there is a corresponding natural period of oscillation. 30-03-2024 Slide No. 18  SIMPLE HARMONIC MOTION – TERMS The amplitude is the maximum distance the mass moves from its equilibrium position. It moves as far on one side as it does on the other. 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 30-03-2024 Slide No. 19  SIMPLE HARMONIC MOTION – PERIOD & AMPLITUDE The key feature of SHM is that the period or frequency of the motion does not depend on the amplitude of the oscillation. From a practical viewpoint this effect was used to make the first accurate clocks A pendulum takes the same time to make one oscillation even though the amplitude of the oscillations dies down with time The period does not change Period T is given by (where L is length) 30-03-2024 Slide No. 20  SIMPLE HARMONIC OSCILLATOR In reality, oscillations do not continue forever – they gradually decrease their motion – energy is lost to friction. You may want the sound caused by a piano or a guitar to continue. But you want the oscillation of your car to stop immediately after going over a bump. Hence the dampers. For any given length of the chain of the swing there is a corresponding natural period of oscillation The period of oscillation does not depend on the mass of the person sitting in the swing. 30-03-2024 Slide No. 21  VIBRATIONS Vibration is a term normally reserved for high frequency periodic motion. Atoms or molecules of a substance vibrate unless the substance is cooled so much that it reaches absolute zero. A tuning fork will vibrate at a known frequency, the characteristic sound wave pattern will produce a predictable sound pitch. In an aircraft, rotating or reciprocal components such as engines and propellers produce vibration which can be annoying and destructive. 30-03-2024 Slide No. 22  VIBRATIONS Vibration experienced in an aircraft may originate from the engines, turbulence, or from flight control flutter due to worn hinges or linkage bearings. The constant vibration is annoying to flight crew and passengers. Also, the structure of the aircraft and other components can vibrate in sympathy and structural damage and component wear can occur. Metal fatigue is an example of such structural damage. 30-03-2024 Slide No. 23  RESONANCE The natural frequency of an object is the frequency where that object vibrates naturally after application of an initial force. 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. 30-03-2024 Slide No. 24  HARMONICS Every object has a natural resonant frequency, at which it vibrates. When a guitar string is plucked, for example, it will vibrate at its natural frequency. Harmonics exist as multiples of the original, natural frequency. If natural (or fundamental) frequency is 100 Hz, this is the 1 st harmonic The 2nd harmonic is at 200 Hz The 3rd at 300 Hz Harmonics can cause resonance as well as natural frequencies. 30-03-2024 Slide No. 25  MECHANICAL ADVANTAGE Work = Force x distance Simple lever system Distances moved in a simple lever system 30-03-2024 Slide No. 26  MECHANICAL ADVANTAGE AND EFFICIENCY There is no perfect machine. There is always friction. Input work is always greater than Output work. Due to friction - some of the input work only produces heat, noise and sparks. Wi = input work Wo = output work Wf = work lost to friction Wi = Wo + Wf 30-03-2024 Slide No. 27  MECHANICAL ADVANTAGE AND EFFICIENCY There are two kinds of Mechanical Advantage. Ideal Mechanical Advantage is what the mechanical advantage would be if there was no friction. It is the ratio of input distance (Di) to output distance (Do). Actual Mechanical Advantage (AMA) is the mechanical advantage in the real world (with friction). It is the Ratio of input force (Fi) to output force (Fo). 𝐷𝑖 𝐹𝑜 IMA = 𝐴𝑀𝐴 = 𝐷𝑜 𝐹𝑖 Efficiency is the ratio of output work to input work. 𝐹𝑜 𝐷𝑜 𝑊𝑜 Eff = = 𝐹𝑖 𝐷𝑖 𝑊𝑖 30-03-2024 Slide No. 28  SIMPLE PULLEY SYSTEMS IMA = the number of strands supporting the load 30-03-2024 Slide No. 29  MORE COMPLEX PULLEY SYSTEMS IMA = the number of strands supporting the load 30-03-2024 Slide No. 30  THE WHEEL AND AXLE 𝑫𝒊 𝟐𝝅𝑹 𝑹 IMA = = = 𝑫𝒐 𝟐𝝅𝒓 𝒓 30-03-2024 Slide No. 31  THE INCLINED PLANE 𝑫𝒊 𝑳 𝟏 IMA = = = 𝑫𝒐 𝒉 𝒉/𝑳 30-03-2024 Slide No. 32  THE SCREW JACK Screw Jack 𝟐𝝅𝒓 IMA = 𝒑 p represents pitch High friction. Low efficiency. However, the distance through which the input force acts in comparison to the pitch is usually very large. This gives a screw jack a large mechanical advantage. 30-03-2024 Slide No. 33  THE HYDRAULIC PRESS 𝝅 𝒓𝟐 𝒅𝒊 = 𝝅 𝑹𝟐 𝒅𝒐 𝒅𝒊 𝑹𝟐 = 𝒅𝒐 𝒓𝟐 𝑹𝟐 𝑰𝑴𝑨 = 𝟐 𝒓 30-03-2024 Slide No. 34  CONCLUSION Now that you have completed this topic, you should be able to: 2.2.2.1 Describe the following aspects of linear movement: uniform motion in a straight line; motion under constant acceleration (motion under gravity). 2.2.2.2 Describe the following aspect of rotational movement: uniform circular motion (centrifugal/centripetal forces). 2.2.2.3 Describe periodic motion and pendular movement. 2.2.2.4 Describe simple theory of the following: vibration; harmonics; resonance. 2.2.2.5 Describe velocity ratio, mechanical advantage and efficiency. 30-03-2024 Slide No. 35  This concludes: Module: B-2 Physics Topic 2.2.2: Kinetics