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Elastic Potential Energy & Hooke’s Law

Elastic Potential Energy & Hooke’s Law. Hooke’s Law.  When work is done to stretch or compress an elastic material like a spring, the material STORES the energy as ELASTIC POTENTIAL ENERGY ( E e ).

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Elastic Potential Energy & Hooke’s Law

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  1. Elastic Potential Energy & Hooke’s Law

  2. Hooke’s Law  When work is done to stretch or compress an elastic material like a spring, the material STORES the energy as ELASTIC POTENTIAL ENERGY (Ee) Linear Elastic Material : the material deformation is DIRECTLY PROPORTIONAL to the applied force Spring 2 Fapp (N) - Spring 2 is “stiffer” then spring 1-it takes more force to produce the same deformation Spring 1 Extension (x) (m)

  3. Spring Constant, K Spring 2 Fapp (N) Spring 1 Slope= K=  Fapp x Units: N/m Extension (x) (m) Stiffer springs have higher Hooke’s Law constants

  4. Restoring Force and Hooke’s Law  The restoring force develops in the spring working against the deforming force A material obeys Hooke’s Law when the magnitude of the restoring force is directly proportional to the deformation of the material. m Fx= kx Fx= kx Fapp

  5. Spring in Equilibrium:When spring is stretched and reaches equilibrium: • Fx= Fapp Fx= kx Fapp • Spring Not in Equilibrium:When spring is in the process of being stretched or compressed it will be accelerating: • Fnet= ma Fx= kx Fapp a Fnet= Fapp - Fx

  6. Example: A mass of 250.0 g, suspended from a vertical spring, causes the spring to stretch to a new equilibrium length with extension of 8.00 cm. What is the spring constant, k? What was the acceleration of the mass as it passed through an extension of 3.0 cm? Ans: 30.6 N/m, 6.13 m/s2

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