Work done by spring with weight to the spring

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SUMMARY

The work done by a spring is expressed as Ws = -0.5kx², where k is the spring constant and x is the displacement. When considering a spring with weight, the total work done is modified to include gravitational effects, resulting in Ws = -0.5kx² - m(spring)g, where m(spring) is the mass of the spring and g is the acceleration due to gravity. The weight of the spring is significant in vertical configurations, while it can be disregarded in horizontal setups due to the nature of conservative forces.

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  • Understanding of Hooke's Law and spring constants
  • Basic knowledge of gravitational forces and potential energy
  • Familiarity with conservative forces in physics
  • Concept of work-energy principle in mechanics
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  • Research the implications of mass on spring dynamics in vertical configurations
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  • Learn about the differences in spring behavior in horizontal vs. vertical orientations
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Hey, I just have a quick question. I understand that the work done by a spring is considered as the following; Ws=-.5kx^2. What if the spring has weight to it? Would the work done by the spring be Ws=-(.5kx^2)-m(spring)g? Does the weight get added or is it not even considered in that equation?

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*i'm saying the weight is the spring, I understand where the weight the spring is holding is associated but what about the mass of the spring if there is one
 
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In the absence of more data, about all you can say about the work done by a spring that is not massless is, since both spring and gravity forces are conservative,
[tex]W_s + W_g = - (\Delta U_s + \Delta U_g)[/tex]. If the spring was horizontal, its mass wouldn't matter, but the case would be different if the spring was vertically mounted.
 

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