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Jakob Littel

Feb 20, 2025

A spring has a spring stiffness constant k of 70.0N/m .?

How much must this spring be compressed to store 50.0J of potential energy?
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2 Answers

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Hermina Ferry

Feb 20, 2025

Or you could understand the physics and derive the equation needed, in which case you'd know when and where to use that equation. The physics and derivation are these:The basic work function, one you should know, is work done = average force X distance the force is applied = F dX (in math talk) By Hooke's thing f = k dX, force applied is proportional to the deformation of the spring, dX. But that's not average force F, which is what we need for the work relationship.However, as the k is constant over the range of dX, we can show that average force F = f/2 = k dX/2 when we start with zero force. [It's F = (ff + fi)/2 = k (dX + dx)/2 when starting with some non-zero force fi already applied.]So we have work = QE = F dX = k dX dX/2 = 1/2 k dX^2 = PE the potential energy stored when QE work is done. And there's your equation. QED.Now plug and chug as Jim has shown you.... Show More
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H
Hermina Ferry

Feb 20, 2025

Use Spring Potential Energy definition formula, substitute knowns and solve for "x"SPE = 1/2kx² {where SPE = 50.0 J, and k = 70.0 N/m}... Show More
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