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CHS: M.Kelly Potential Energy and Conservation of Energy
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CHS: M.Kelly Potential Energy Potential energy (U): energy that can be associated with the configuration (or arrangement) of system of objects that influence one another. –Gravitational potential energy, Ug –Elastic potential energy, Ue ΔU = - W
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CHS: M.Kelly Conservative and Nonconservative Forces The system consists of two or more objects A force acts between a particle-like object (e.g. block) in the system and the rest of the system. When the system configuration changes, the force does work (W 1 ) on the object. When the configuration change is reversed, the force reverses the energy transfer, doing work (W 2 ) in the process. Conservative force: W 1 = - W 2
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CHS: M.Kelly Path of Independence of Conservative Forces The net work done by a conservative force on a particle moving around every closed path is zero. The work done by a conservative force on a particle between two points does not depend on the path taken by the particle.
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CHS: M.Kelly
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Potential energy values Gravitational Potential Energy Depends only on the vertical position (or height) of the particle relative to the reference position (y=0) Choose reference configuration to be zero height (object at y i =0) Elastic Potential Energy Example: spring and block system Choose the reference configuration to be when spring is relaxed (block at x i =0)
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CHS: M.Kelly Conservation of Mechanical Energy Mechanical Energy, E mec, of a system is the sum of potential and kinetic energy: E mec = K + U (mechanical energy) K 2 + U 2 = K 1 + U 1 (conservation of mechanical energy) –Only in an isolated system where conservative forces cause energy changes.
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CHS: M.Kelly
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Energy Transformation on a Roller Coaster
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CHS: M.Kelly If the potential energy function U is known, the force at any point can be obtained by taking the derivative of the potential.
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CHS: M.Kelly If the force is known, and is a conservative force, then the potential energy can be obtained by integrating the force.conservative forcepotential energy
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CHS: M.Kelly Reading the potential energy curve For one-dimensional motion, the work done is a function of the F(x) and the distance, Δx Examine turning points: K=0 (since U = E) Particle changes direction Look for equilibrium points: Are they neutral, Stable, or Unstable.
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CHS: M.Kelly Work done on a system by an external force. Work is energy transferred to or from a system by means of an external force acting on the system. No friction involved: W = ΔK + ΔU W = Δ W mech Considering friction: F – f k = ma Fd = Δ E mech + f k d Δ E th = f k d (increase in thermal energy by sliding) W = Δ E mech + Δ E th (work done on system, friction involved)
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CHS: M.Kelly Energy Transformation for Downhill Skiing Work done on a system by an external force. K initial + U initial + W external = K final + U final
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CHS: M.Kelly Conservation of Energy The total energy (E) of a system can change only by energy transferred to or from the system. W = ΔE = ΔE mech + ΔE th + ΔE int. Remember: ΔE mech are changes in ΔK and ΔU Isolated system: the total energy, E, of the system can not change. 0 = ΔE mech + ΔE th + ΔE int. (isolated system) ΔE mech-2 = ΔE mech-1 - ΔE th - ΔE int. We can related the total energy at one instant another instant without considering the energies at intermediate times. Examine Sample Problems 8-7, 8-8.
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