Lecture_17

Lecture_17 - 10.3 Potential Energy of a Spring Elastic...

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10.3 Potential Energy of a Spring – Elastic Potential Energy The elastic restoring force, like gravity, is a conservative force . Therefore, we can define a potential for the elastic restoring force, and thus a potential energy . et a spring force move a mass om Let a spring force move a mass m from x o to x f . m m x o x f What is the work done by the spring in moving the mass from x o to x f ? We know the work done by a constant force is d F W d = But, the spring force is not constant, since it depends on x . ) ( ) ( x F x F + Instead, we use the average force to compute the work: 2 f o F = Result: 2 2 1 2 2 1 f o kx kx W =
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This is analogous to the result we found for the work done by gravity: gh gh f o mgh mgh W = In the gravitational case, the gravitational PE is: mgh = G PE For the spring force: 2 2 1 E PE kx = This is the Elastic Potential Energy . The elastic PE, like the gravitational PE, is energy of position. It depends on x , which is relative to some arbitrary zero, usually the unstretched length of the spring. Now we have still another term that can contribute to the total mechanical energy: ot rans PE PE KE KE E + + + = E G Rot Trans 2 2 1 2 2 1 2 2 1 E kx mgh I mv + + + = ω
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Example : A mass of 15 kg is attached to one end of a spring (k = 325 N/m) and is free to slide on a frictionless horizontal surface. The mass is pulled back 0.75 m from its equilibrium position and released. Find the speed of the mass as it passes back thru the qp p p equilibrium position.
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Lecture_17 - 10.3 Potential Energy of a Spring Elastic...

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