ch6 - Work and Energy Chapter Outline GENERAL PHYSICS PHY...

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Unformatted text preview: Work and Energy Chapter Outline GENERAL PHYSICS PHY 302K Work Done by a Constant Force Work Done by a Varying Force Chapter 6: Work and Energy Kinetic Energy and the Work-Energy Principle Potential Energy Maxim Tsoi Conservative and Nonconservative Forces Energy Conservation Power Physics Department, The University of Texas at Austin http://www.ph.utexas.edu/~tsoi/302K.htm 302K - Ch.6 302K - Ch.6 Work Done by a Constant Force Work Done by a Varying Force Concept of work • The work W done on a system by an agent exerting a constant force on 1D displacement of a particle • Particle is displaced along the x axis under the action of a force Fx that varies with position the system is the product of the force’s magnitude F, the magnitude r W Fx x of the displacement of the point of application of the force, and cos, xf W Fx x where is the angle between the force and displacement vectors: xi xf W lim Fx x W F r cos x 0 xi • If more than one force acts on a system and • Work scalar quantity the system can be modeled as a particle: • The SI unit of work newton meter (N m)= joule (J) Wnet W • Work is an energy transfer to or from the system 302K - Ch.6 302K - Ch.6 Systems and Environments Conservation of Energy System, its boundary, and environment Isolated system vs Nonisolated system • Isolated system does not interact with its environment • System a small portion of the Universe • may be a single object or particle • Types of energy that system can possess kinetic, internal, potential • Ways to transfer energy into or out of a system: • may be a collection of objects or particles • Work • may be a region of space • Mechanical waves • may vary in size and shape • Heat • Matter transfer • System boundary an imaginary surface that divides the Universe into the system and the surrounding environment • Electrical Transmission • Electromagnetic radiation We can neither create nor destroy energy energy is always conserved E system T Total amount of energy in a system changes energy has crossed the boundary of the system by one of the energy transfer mechanisms 302K - Ch.6 302K - Ch.6 1 Work Done by a Varying Force Kinetic Energy Work done by a spring Work-kinetic energy theorem A block on a horizontal, frictionless surface is connected to a spring • One of possible outcomes of doing work on a system system changes its speed • Kinetic energy type of energy (associated with motion) that a system can possess • Force on the block (Hook’s law): Fs kx W F x ma x 1 2 mv 2 1 mv i2 f 2 ( v v 2ax ) 2 f 2 i k spring constant • Work done by the spring force on the block: K W 1 kxi2 1 kx 2 f 2 2 mv 2 2 • In the case in which work is done on a system and the only change in the system is in its • Work done by an external force Fapp: speed, the work done by the net force equals the change in kinetic energy of the system W 1 kx 2 1 kxi2 f 2 2 W K Example 6.2 302K - Ch.6 Potential Energy of a System Earth) as the book undergoes an upward displacement: Conservation of Mechanical Energy The isolated system • Work done on the book by the gravitational force as the book falls: Won book mgyb mgya W Fr cos mgyb mgya • Gravitational potential energy is identified as: U g mgy • Work done on the system appears as a change in the potential energy of the system: W U g • Gravitational potential energy depends only on the vertical height of the • The change in book’s kinetic energy (work-kinetic energy theorem): K book Won book mgy b mgy a U i U f U g • Mechanical energy is the sum of kinetic and potential energies: object above the surface of the Earth W Fr cos mgy b mgy a • The difference in potential energy is important the choice of reference configuration is arbitrary 302K - Ch.6 K i K 302K - Ch.6 Gravitational potential energy • Work done by an external agent on the system (book and f E mech K U • Mechanical energy of an isolated system is conserved! K U 0 K f K i U f U i K f U f Ki Ui mv 2 mgy const 2 Example 6.4-5 302K - Ch.6 Conservation of Mechanical Energy Conservative and Nonconservative Forces Elastic potential energy • Work done by an external applied force on the system of block and spring is given by: WFapp kx kx 1 2 2 f 1 2 2 i Conservative forces • The work done by a conservative force on a particle moving between any two points is independent of the path taken by the particle • The work done by a conservative force on a particle moving through any closed path (beginning and end points are identical) is zero nonconservative force • The elastic potential energy is defined as: U s 1 kx 2 – does not satisfy the above properties – cause a change in Emech 2 Wnc Emech is zero whenever the spring is undeformed always positive in a deformed spring 302K - Ch.6 302K - Ch.6 2 Power SUMMARY Work and Energy Time rate of energy transfer • Work done on a system by an agent exerting force F: • If an external force is applied to an object, and if the work done by this force in the time interval t is W, then the average power during this interval is defined as: • Instantaneous power is the limiting value of the average power as t 0 W r P F v F t t • Power is defined for any type of energy transfer • The SI unit of power: joules per second = watt (W) • The U.S. customary system’s unit: horsepower (1 hp=746 W) • A unit of energy can now be defined as kilowatt-hour P W t P lim t 0 W t • Kinetic energy: K mv 2 • Work-kinetic energy theorem: • Gravitational potential energy: E P t • Mechanical energy: W K f K i K U g mgy E mech K U • Law of conservation of mechanical energy: • Elastic potential energy: K f U f Ki Ui U s 1 kx 2 2 (1 kWh=3.60106 J) • Power time rate of energy transfer: 302K - Ch.6 W F r cos 2 P dE dt 302K - Ch.6 3 ...
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This note was uploaded on 09/01/2009 for the course PHY M taught by Professor Staff during the Spring '09 term at University of Texas.

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