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UT Arlington PHYS 1443 - Lecture 8 Work and Kinetic Energy

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1443-501 Spring 2002 Lecture #8Work and Kinetic EnergyEnergy Loss in AutomobileExample 7.14Kinetic Energy at High SpeedPotential EnergyGravitational PotentialExample 8.1Elastic Potential EnergyConservative and Non-conservative ForcesMore on Conservative and Non-conservative ForcesConservative Forces and Potential Energy1443-501 Spring 2002Lecture #8Dr. Jaehoon Yu1. Work and Kinetic Energy2. Energy Loss in Automobile 3. Potential Energy 4. Conservative and Non-conservative Forces5. Conservative Forces and Potential EnergyFeb. 18, 2002 1443-501 Spring 2002Dr. J. Yu, Lecture #82Work and Kinetic EnergyWork in physics is done only when a sum of forces exerted on an object made a motion to the object.What does this mean?However much tired your arms feel, if you were just holding an object without moving it you have not done any physical work.Mathematically, work is written in scalar product of force vector and the displacement vector Kinetic Energy is the energy associated with motion and capacity to perform work. Work requires change of energy after the completion Work-Kinetic energy theoremUnits of these quantities????Power is the rate of which work is performed.cosFddFWi221mvK  vFsdtdFdtdWP KKKWifNm=JouleNm/s=Joule/s=WattFeb. 18, 2002 1443-501 Spring 2002Dr. J. Yu, Lecture #83Energy Loss in AutomobileAutomobile uses only at 13% of its fuel to propel the vehicle. Why?67% in the engine: 1. Incomplete burning2. Heat 3. Sound13% used for balancing energy loss related to moving vehicle, like air resistance and road friction to tire, etcTwo frictional forces involved in moving vehicles kWNvfPt5.188.26691 NmgnNmgWeightkgmcar22714200 ,1450Coefficient of Rolling Friction; =0.01616% in friction in mechanical parts4% in operating other crucial parts such as oil and fuel pumps, etcAir Dragartfff 222647.02293.15.02121vvAvDfaTotal ResistanceTotal power to keep speed v=26.8m/s=60mi/hPower to overcome each component of resistance kWvfPrr08.68.26227  kWvfPaa5.128.267.464 Feb. 18, 2002 1443-501 Spring 2002Dr. J. Yu, Lecture #84Example 7.14A compact car has a mass of 800kg, and its efficiency is rated at 18%. Find the amount of gasoline used to accelerate the car from rest to 27m/s (~60mi/h). Use the fact that the energy equivalent of 1gal of gasoline is 1.3x108J. JmvKf522109.2278002121Then using the fact that 1gal of gasoline can putout 1.3x108J, we can compute the total volume of gasoline needed to accelerate the car to 60 mi/h.First let’s compute what the kinetic energy needed to accelerate the car from rest to a speed v.Since the engine is only 18% efficient we must divide the necessary kinetic energy with this efficiency in order to figure out what the total energy needed is.JJmvKWfE552101618.0109.221galgalJJgalJWVEga s012.0/103.11016/103.1858Feb. 18, 2002 1443-501 Spring 2002Dr. J. Yu, Lecture #85Kinetic Energy at High SpeedThe laws of Newtonian mechanics is no longer valid for object moving at the speed close to that of light, c. It must be more generalized for these special cases. Theory of relativity. The kinetic energy must be modified to reflect the fact that the object is moving very high speed.The speed of an object cannot be faster than light in vacuum.  Have not seen any particle that runs faster than light, yet.However this equation must satisfy the Newtonian expression!!  11122cvmcKWhat does this expression tell you? 2222242222212112111...83211111mvcvmccvmccvcvmccvmcKFeb. 18, 2002 1443-501 Spring 2002Dr. J. Yu, Lecture #86Potential EnergyEnergy associated with a system of objects  Stored energy which has Potential or possibility to work or to convert to kinetic energyWhat does this mean?In order to describe potential energy, U, a system must be defined.What other forms of energies in the universe?The concept of potential energy can only be used under the special class of forces called, conservative forces which results in principle of conservation of mechanical energy.Mechanical EnergyBiological EnergyElectromagnetic EnergyNuclear EnergyChemical EnergyFeb. 18, 2002 1443-501 Spring 2002Dr. J. Yu, Lecture #87Gravitational PotentialWhen an object is falling, gravitational force, Mg, performs work on the object, increasing its kinetic energy. The potential energy of an object at a height y which is the potential to work is expressed asPotential energy given to an object by gravitational field in the system of Earth due to its height from the surfacemyfmmgyi   mgyjyjmgyFUggWhat does this mean?gfifigUmgymgyUUWWork performed on the object by the gravitational force as the brick goes from yi to yf is:Work by the gravitational force as the brick goes from yi to yf is negative of the change in the system’s potential energymgyUgFeb. 18, 2002 1443-501 Spring 2002Dr. J. Yu, Lecture #88Example 8.1A bowler drops bowling ball of mass 7kg on his toe. Choosing floor level as y=0, estimate the total work done on the ball by the gravitational force as the ball falls.  JJUUUJmgyUJmgyUifffii3024.3206.203.08.973.345.08.97b) Perform the same calculation using the top of the bowler’s head as the origin.Assuming the bowler’s height is 1.8m, the ball’s original position is –1.3m, and the toe is at –1.77m.MLet’s assume the top of the toe is 0.03m from the floor and the hand was 0.5m above the floor.What has to change?   JJUUUJmgyUJmgyUifffii302.324.12177.18.972.893.18.97First we must re-compute the positions of ball at the hand and of the toe.Feb. 18, 2002 1443-501 Spring 2002Dr. J. Yu, Lecture #89Elastic Potential EnergyThe force spring exerts on an object when it is distorted from its equilibrium by a distance x isPotential energy given to an object by a spring or an object with elasticity in the system consists of the object and the spring without friction.kxFsWhat do you see from the above


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UT Arlington PHYS 1443 - Lecture 8 Work and Kinetic Energy

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