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Unformatted text preview: :now much energy can be stored in a spring with j,,= 320 Njm if the maximum allowed stretch is 126 CHAPTER8 where the spring has its natural length the unstretchedposition (A). (a) At equilibrium (B), kx = mg, so the potential energy of just the spring is Us(B) = !kx2 = !k(mgjk)2 = 0.5(3 kgx9.8 m/s2)2 + (240 N/m) = 1.80 J. (b) The change in just the gravitational potential energy between the equilibrium and unstretehed positions is dU:A = Ug(A) Ug(B) = mgx = mg(mg/k) = 3.60J. (c) The corresponding change in the spring's potential energy is L:i.U{3A= Us(A)  Us (E.) = 0  1.80 J. Although the change in the total potential energy,L:i.UBA = AU:A + AU{3A = 3.60 J '1.80 J = 1.80 J, is not zero, there is no discrepancy. In order to move the fish slowly upward, you would have to exert an upward applied force (Fa mg  kx) that would do work W!A == mgx kx2 = dU BA, as required by the workenergy theorem. Solution
For a onedimensional force, one can use Equation to find U(x)  U(O) = _fJ5cm(kx  cx3)dx! = 82a l!kx 2 + ~cx41~5cm=
3 i(3.6 kN/m )(0.15 could be recaptured from the spring...
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 Spring '08
 WORMER
 Physics, Conservation Of Energy, Energy, Work

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