2012_1061_Lecture_Ch_078

A system not an object potential energy continued

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Unformatted text preview: WG = mg (y2 − y1 )  The gravitational potential energy, U is defined by Ugrav = mgy  Caveats: [gravity only] Change in potential energy is what is physically meaningful Potential energy belong to a system not an object Potential Energy (continued)  Potential Energy in General ∆U = −WG = − ￿ 2 1 − → − → FG · d ￿  There are other types of potential energies besides gravitational. We can define a potential energy only for conservative forces ∆U = U2 − U1 = − ￿ 1 2 −− →→ F · d ￿ = −W Elastic Potential Energy Fp = +kx Force of a person pushing Fs = −kx ∆U = U (x) − U (0) = − ￿ 1 2 Force of the spring pushing back − → − → Fs · d ￿ = − 12 Uel (x) = kx 2 ￿ x 0 12 (−kx)dx = kx 2 [elastic spring] Mechanical Energy and Its Conservation  Consider a conservative system( where only conservative forces do work) in which energy is transformed from kinetic to potential and vice versa ➥ Mass at the end of a spring ➥ Mass moving in the Earth gravitational field  According to the work-Energy principle ∆Utotal Wnet = ∆K ￿2 − →...
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