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Problem 1 Imagine a spring that doesn't follow Hooke's law, but instead requires a force F(x) to deform (here x is the amount of deformation and k is a constant). Suppose you want to stretch the spring from x = 0 (equilibrium) to x = Xo. All answers in this problem should be given symbolically in terms of the constants k and xo. kx3 (a) Calculate the work required to stretch the spring from x = 0 to x = 0.5xo. (b) Calculate the work required to stretch the spring from x = 0.5xo to x = Xo. (c) Find the potential energy function for this force, U(x), where x = 0 is the zero point.

Problem 1 Imagine a spring that doesn't follow Hooke's law, but instead requires a force F(x) to deform (here x is the amount of deformation and k is a constant). Suppose you want to stretch the spring from x = 0 (equilibrium) to x = Xo. All answers in this problem should be given symbolically in terms of the constants k and xo. kx3 (a) Calculate the work required to stretch the spring from x = 0 to x = 0.5xo. (b) Calculate the work required to stretch the spring from x = 0.5xo to x = Xo. (c) Find the potential energy function for this force, U(x), where x = 0 is the zero point.

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Problem 1 Imagine a spring that doesn't follow Hooke's law, but instead requires a force F(x) = kx3 to deform (here x is the amount of deformation and k is a constant). Suppose you want to stretch the spring from x = 0 (equilibrium) to x = Xo. All answers in this problem should be given symbolically in terms of the constants k and xo. %3D (a) Calculate the work required to stretch the spring from x = 0 to x = 0.5xo. (b) Calculate the work required to stretch the spring from x = 0.5xo to x = Xo. (c) Find the potential energy function for this force, U(x), where x = 0 is the zero point. %3D %3D
Transcribed Image Text:Problem 1 Imagine a spring that doesn't follow Hooke's law, but instead requires a force F(x) = kx3 to deform (here x is the amount of deformation and k is a constant). Suppose you want to stretch the spring from x = 0 (equilibrium) to x = Xo. All answers in this problem should be given symbolically in terms of the constants k and xo. %3D (a) Calculate the work required to stretch the spring from x = 0 to x = 0.5xo. (b) Calculate the work required to stretch the spring from x = 0.5xo to x = Xo. (c) Find the potential energy function for this force, U(x), where x = 0 is the zero point. %3D %3D
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