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 WorkEnergy 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 Workkinetic 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 (workkinetic 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 6.45 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 kilowatthour P W
t P lim t 0 W
t • Kinetic energy: K mv
2 • Workkinetic 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.
 Spring '09
 Staff
 Physics

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