Candelario Christiansen
Feb 08, 2025
A spring has a spring stiffness constant k of 70.0N/m .?
What compression is required for a spring with a stiffness constant (k) of 70.0 N/m to store 50.0 J of potential energy?
2 Answers
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.
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