Lecture Notes on Energy - University of Nicosia, PDF

Energy Dr Anastasia Hadjiconstanti Prof Vered Aharonson  LECTURE LOB’S 13.DESCRIBE THE CONCEPTS OF WORK, ENERGY, POWER AND MECHANICAL EFFICIENCY. 14.DESCRIBE THE CONCEPTS OF KINETIC AND POTENTIAL ENERGY. 16. EXPLAIN CONSERVATION OF ENERGY. ...

Energy Dr Anastasia Hadjiconstanti Prof Vered Aharonson  LECTURE LOB’S 13.DESCRIBE THE CONCEPTS OF WORK, ENERGY, POWER AND MECHANICAL EFFICIENCY. 14.DESCRIBE THE CONCEPTS OF KINETIC AND POTENTIAL ENERGY. 16. EXPLAIN CONSERVATION OF ENERGY.  WHAT IS ENERGY? https://sciencenotes.org/energy-definition-examples/  WORK I Work is one process by which energy is transferred from one form to another. Work describes how much energy is transferred from one form to another, and what sort of process was involved Mechanical, gravitational, electrical, light, sound, heat, chemical, nuclear. In example, a falling object gains kinetic energy and loses potential energy, and this transformation occurs because the gravity of the Earth does work on the object. In the absence of other forces such as air resistance acting on the object, the work done by the gravity is the increase in the kinetic energy of the object.  WORK II Work Done By A Constant Force You do work when you push an object up a hill. üThe longer the hill the more work you do: more distance. üThe steeper the hill the more work you do: more force. The work done on an object by a constant force (constant in both magnitude and direction) is defined as the product of the magnitude of the displacement times the component of the force parallel to the displacement. W = F/ / × d 6  WORK III Work Done By A Constant Force We can also write: W = F// × d = F d cos q where F is the magnitude of the constant force, d is the magnitude of the displacement of the object, and 𝜃 is the angle between the directions of the force and the displacement. The work done by a force which produces a displacement which is not in the same direction as the force.  WORK IV Work Done By A Constant Force Work is a scalar quantity – it has no direction, only magnitude, which can be positive or negative. W = F d cosq = F// × d If 𝜃 = 0o then W > 0 If 𝜃 = 180o then W < 0 (e.g friction) If 𝜃 = 90o then W = 0 A force does positive work when it has a vector component in the same direction as the displacement, and it does negative work when it has a vector component in the opposite direction. It does zero work when it has no parallel vector component or no displacement. 8  WORK V Work Done By A Constant Force In SI units work is measured in newton-meters (N.m). A special name is given to this unit, the joule (J): Units: 1 N.m = 1 J (Joule)  WORK VI When a force does no work W = F d cosq = F// × d  WORK VII Work Done By A Constant Force With work, as with force, it is necessary to specify if the work was done by a specific object or done on a specific object. It is also important to specify whether the work done is due to one particular force (and which one), or the total (net) work done by the several forces.  KINETIC ENERGY I An object in motion has the ability to do work and thus can be said to have energy. The energy of motion is called kinetic energy. 1 𝐾𝐸 = 𝑚𝑣 ! 2 https://sciencenotes.org/energy-definition-examples/  KINETIC ENERGY IV Because of the direct connection between work and kinetic energy, energy is measured in the same units as work: joules is SI units 1 2 KE = mv Units: kg.m2/s2 = J (Joule) 2 Like work, kinetic energy is a scalar quantity. CLASS EXAMPLE 1 A man pushes on a car with a force of 300 N and moves it 10 m (in the direction of the force). This is shown in Figure below. How much work is done by the man on the car? Solution: The applied force and the displacement that is produced by the force are in the same direction 𝐖 = 𝑭𝒅𝒄𝒐𝒔𝜽 = 𝑭𝒅𝒄𝒐𝒔 𝟎𝑶 = 𝑭𝒅 = 𝟑𝟎𝟎𝑵 𝒙 𝟏𝟎𝒎 = 𝟑𝟎𝟎𝟎𝑱 This technique may be used to calculate the work done by the force whether or not there is friction and whether or not the car accelerates.  POTENTIAL ENERGY I Kinetic energy is the energy of an object as a result of its motion. Potential energy is the energy of an object as a result of its position or configuration relative to the surroundings. Each type of potential energy (PE) is associated with a particular force. https://www.inspiritvr.com/general-physics/conservation- laws/potential-energy-study-guide  POTENTIAL ENERGY II Gravitational Potential Energy A heavy brick held high above the ground has potential energy because of its position relative to the Earth. The raised brick has the ability to do work, for if it is released, it will fall to the ground due to the gravitational force, and can do work on, say, a stake, driving into the ground. https://www.inspiritvr.com/ge neral-physics/conservation- laws/potential-energy-study- guide  POTENTIAL ENERGY III Gravitational Potential Energy For an object of mass m to be lifted vertically, an upward force at least equal to its weight, mg, must be exerted on it (say, by a person’s hand). To lift the object without acceleration, the person exerts an “external force” Fext = mg. If it is lifted through a vertical height h, from position A to B, a person does work equal to the product of the “external” force she exerts, Fext = mg upward, multiplied by the vertical displacement h: 𝑾 = 𝑭𝒅𝒄𝒐𝒔𝜽 = 𝑭𝒅𝒄𝒐𝒔 𝟎𝑶 = 𝒎𝒈𝒉 The increase in the gravitational potential energy is provided by the input of work from the external force. This means that the gain in potential energy is: 𝑷𝑬𝒈𝒓𝒂𝒗𝒊𝒕𝒂𝒕𝒊𝒐𝒏𝒂𝒍 = 𝒎𝒈𝒉  POTENTIAL ENERGY IV Gravitational Potential Energy The gravitational potential energy associated with a particle – Earth system depends only on the vertical position y (or height) of the particle relative to the reference position y = 0, NOT on the horizontal position.  POTENTIAL ENERGY VI With gravitational force, the work done by gravitational force is independent of path. It depends only on the initial and final positions yf f h Wgif= - mg(yf- yi) yi i mg So if we move a mass from any position and go around and then back to the starting point the work done by gravity is zero.  CONSERVATIVE FORCES I If the work done by a force does not depend on the path taken this force is called a conservative force. Wab ,1 = Wab ,2  DISSIPATIVE (NON – CONSERVATIVE) FORCES Work done by friction x W1®2 = f × x × cos180 = - f × x f 1 2 x W2®1 = f × x × cos180 = - f × x f 2 1 Wnet = W1®2 + W21®1 = -2 f × x ¹ 0 ! 21  CONSERVATIVE AND NON - CONSERVATIVE FORCES Conservative and Non - conservative Forces Conservative Forces Non - conservative Forces Gravitational Friction Elastic Air resistance Electric Tension in cord Push or pull by a person üCheckpoint The figure shows three paths connecting points α and b. A single force F does the indicated work on a particle moving along each path in the indicated direction. On the basis of this information, is force F conservative? üNO! The force is conservative when any choice of path between the points gives the same amount of work and a round trip gives a total work of zero.  CONSERVATIVE FORCES II Potential Energy (PE) or U Because potential energy is associated with the position or configuration of objects, It must be stated uniquely for a given point. This cannot be done with non - conservative forces because the work done depends on the path taken. Hence, potential energy can be defined only for a conservative force, not all forces have a potential energy. In example, there is no potential energy for friction.  MECHANICAL ENERGY The total mechanical energy of a system is defined as the sum of the kinetic and potential energies at any moment. EMEC = KE + PE A non conservative force removes mechanical energy from the system under consideration. Forces which do not do this are called conservative. Conservative forces are those which do not change the amount of mechanical energy in the system.  CONSERVATION OF MECHANICAL ENERGY I The Principle of the Conservation of Energy: The total amount of energy in a closed system does not increase or decrease. A closed system is one which does not exchange energy with its surroundings. Energy can be transformed from one form to another and transferred from one object to another, but the total amount remains constant. https://www.solarschools.net/knowledge-bank/energy https://www.youtube.com/watch?v=mhIOylZMg6Q&ab_cha nnel=hamedthelord  CONSERVATION OF MECHANICAL ENERGY II Work done by friction and loss of mechanical energy If we send a block sliding across the ground it will certainly stop after travelling a certain distance. What happened to the lost mechanical energy? We know from experience that whenever two surfaces slide against each other their temperature is increased. In a good approximation the lost mechanical energy which is equal to the work done by friction is transformed into thermal energy that we could measure with a sensitive thermometer. DEthermal » W friction  CONSERVATION OF MECHANICAL ENERGY III Work done by friction and loss of mechanical energy The change ΔEthermal is the magnitude of the frictional force multiplied by the magnitude d of the displacement caused by the external force by ΔE!" = 𝑓#$%&#'% 𝑑 CLASS EXAMPLE 2 Suppose that 0.3 kg ball is dropped a vertical distance of 7 m. What its final speed? Solution: 𝑲𝑬𝒇 + 𝑷𝑬𝒇 = 𝑲𝑬𝒊 + 𝑷𝑬𝒊 𝟏 𝟐 𝒎 𝟎. 𝟑 𝒌𝒈 𝒙 𝒗 + 𝟎 𝑱 = 𝟎 𝑱 + 𝟎. 𝟑 𝒌𝒈 𝒙𝟗. 𝟖𝟏 𝟐 𝒙𝟕𝒎 𝟐 𝒔 𝒎 𝟎. 𝟑 𝒌𝒈 𝒙 𝟗. 𝟖𝟏 𝟐 𝒙𝟕𝒎 𝒗𝟐 = 𝒔 𝒙 𝟐 = 𝟏𝟑𝟕𝒎𝟐 𝒔-𝟐 𝟎. 𝟑 𝒌𝒈 𝒗 = 𝟏𝟑𝟕𝒎𝟐 𝒔-𝟐 = 𝟏𝟏. 𝟕 𝒎/𝒔 CLASS EXAMPLE 3 A very small bus, with a mass of 500 kg, travels down a slope as shown in the figure below and arrives at the bottom of the slope travelling at a speed of v = 15 m/s. The slope is 87.5 m long and starts at 20 m above the end point. Calculate the average force of friction on the bus. Solution: We begin by setting the reference point at the base of the slope 𝑲𝑬𝒇 + 𝑷𝑬𝒇 = 𝑲𝑬𝒊 + 𝑷𝑬𝒊 + 𝑾𝒇𝒓𝒊𝒄𝒕𝒊𝒐𝒏 𝟏 𝒙𝟓𝟎𝟎 𝒌𝒈 𝒙(𝟏𝟓)𝟐 +𝟎 𝑱 = 𝟎 + 𝟓𝟎𝟎 𝒌𝒈 𝒙 𝟗. 𝟖𝟏 𝒎 𝒔-𝟐 𝐱 𝟐𝟎𝒎 + 𝑾𝒇𝒓𝒊𝒄𝒕𝒊𝒐𝒏 𝟐 𝑾𝒇𝒓𝒊𝒄𝒕𝒊𝒐𝒏 = 𝟓𝟔𝟐𝟓𝟎 − 𝟗𝟖𝟏𝟎𝟎 = −𝟒𝟏𝟖𝟓𝟎 𝑱 𝑾𝒇𝒓𝒊𝒄𝒕𝒊𝒐𝒏 𝟒𝟏𝟖𝟓𝟎𝑱 𝑾𝒇𝒓𝒊𝒄𝒕𝒊𝒐𝒏 = 𝒇𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒅 → 𝒇𝒂𝒗𝒆𝒓𝒂𝒈𝒆 = = = 𝟒𝟕𝟖 N 𝒅 𝟖𝟕.𝟓𝒎  POWER I Power is defined as the rate at which work is done. The power equals the work done divided by the time to do it. 𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒 𝑃𝑜𝑤𝑒𝑟 = 𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 or using mathematical symbols 𝑊 𝑃= Δt The power rating of an engine refers to how much chemical or electrical energy can be transformed into mechanical energy per unit time.  POWER II In SI units, power is measured in joules per second, and this unit is given a special name, the watt (W): 1 W = 1 J/s Take care NOT to confuse this with the variable W which is work, measured in J. Since the power is the work done per second, we are able to rewrite the definition so that it is a little more useful for solving many problems: 𝑊 𝐹𝑑 𝑑 𝑃= = =𝐹 Δ𝑡 Δ𝑡 Δ𝑡 𝑷 = 𝑭𝒗  POWER III Power output of the human body in various activities  CLASS EXAMPLE 4 A 70 kg man runs up a flight of stairs 3 m high in 2 s. What is the average power he produces in order to achieve this? Solution: The man must do work against gravity in order to raise his centre of gravity the required 3 m 𝑊!""#$%& = ΔΚΕ + ΔPE = 0 𝐽 + ΔPE = 𝑚𝑔ℎ = 70 𝑘𝑔 𝑥 9.81 𝑚𝑠 '( 𝑥 3 𝑚 = 2060 𝐽 𝑊 2060 𝐽 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑜𝑤𝑒𝑟 = = = 1030 𝑊 Δt 2𝑠 The total power output is 1030 W. This is substantial power output for a human, given that the baseline metabolic rate is about 100 W and playing basketball requires a power output of about 800 W.  MECHANICAL EFFICIENCY I Assumption for power output: all of the energy provided to a machine is effectively utilised as work. The human body is a machine powered by the body’s metabolism. No real machine conforms exactly to this ideal! In real-world cases, some of the energy input into the machine is wasted by the machine - does not output work - since at least some will be lost to dissipative forces. There will always be some waste heat or sound generated by a real machine. To quantify this issue, an mechanical efficiency, n, of a machine is defined as: 𝑊𝑜𝑟𝑘 𝑜𝑢𝑡 𝑊𝑜𝑟𝑘 𝑜𝑢𝑡𝑝𝑢𝑡 𝑛 = 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = = 𝑊𝑜𝑟𝑘 𝑖𝑛 𝐸𝑛𝑒𝑟𝑔𝑦 𝑢𝑠𝑒𝑑 CLASS EXAMPLE 5 At what rate is energy being produced by a cyclist when cycling with a power of 370 W and a bicycle mechanical efficiency of 20%? Solution: 20 𝑝𝑜𝑤𝑒𝑟 𝑜𝑢𝑡 370 𝑊 20% = = 0.2 = 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = = 100 𝑝𝑜𝑤𝑒𝑟 𝑖𝑛 𝑃;< 370 𝑊 𝑃;< = = 1850 𝑊! 0.2 Again compare this energy with a value of about 800 W which is required to play basketball. EXERCISE FOR HOME For the questions bellow, answer if the statement is true or false 1. A force applied to keep an object stationary does no work. qTrue qFalse 2. The potential energy of an object depends on the strength of the gravitational field. qTrue qFalse 3. When a body is falling freely under the influence of gravity, the kinetic energy remains constant. qTrue qFalse  SUMMARY I Energy: The capability of a system to do work on another system. The SI unit of energy is the joule (J). 1𝐽 = 1 𝑁. 𝑚 = 1 𝑘𝑔𝑚( 𝑠 '(. Work: The transfer of energy from one system to another. Particularly, in the case where a force causes a body to move in the direction of the force. Kinetic Energy (KE): Energy that an object has by virtue of its motion. Potential Energy (PE or U): Energy that an object has by virtue of its position. Mechanical Energy: The sum of the kinetic and potential energy of a system.  SUMMARY II Dissipative (non-conservative) force: A force that removes mechanical energy from a system, I.e. friction forces convert mechanical energy from a system, I.e. gravity. Conservation of total energy: The total amount of energy in a system does not change when there are no dissipative forces acting. Energy is never created or destroyed it is only transformed between the different types of energy. Dissipative forces do not destroy energy, they remove it from the system being considered. Power (P): The amount of work done divided by the time it takes to do this work. It is the rate at which work is done. Mechanical efficiency: The proportion of the output work that is provided by a machine to the input work provided to it.  REFERENCES Authors Title Edition Publisher Year ISBN Kirsten Franklin, Paul Introduction to Biological John Wiley & Muir, Terry Physics for the Health and 1st Edition 2010 9780470665930 Sons Scott and Pa Life Sciences ul Yates I.P. Herman Physics of the Human Body 2nd Edition Springer 2016 978331923930 Martin Zinke Cengage Physics of the Life Sciences 3rd Edition 2016 9780176558697 Allmag Learning R.K.Hobbie Intermediate Physics for 5th Edition Springer 2015 9783319126814 and B.J.Roth Medicine and Biology Physics in Biology and Academic P. Davidovits 4th Edition 2012 9780763730406 Medicine Press