Why Does a Spring's Work Calculation Include a Factor of 1/2?

AI Thread Summary
The calculation of a spring's work includes a factor of 1/2 because the spring force is variable, not constant. To find the work done, one must integrate the force, represented as F = kx, from 0 to x. This integration results in the formula for potential energy in a spring, PE_spring = 1/2 k x^2. For those unfamiliar with calculus, explaining the concept using the average force exerted by the spring during compression or stretching can be effective. Visual aids, like a force vs. displacement graph, can help clarify this concept for students.
Nick G
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if W = Fd

and F = kx

then W = kx^2 ?

where does the 1/2 in PEspring = 1/2 k x^2 come from...

F not constant when applied to a spring?

i know it has something to do with the integration but my high school kids have yet to take calc

help please
 
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The spring force is a variable force. Therefore you must integrate kx dx from 0 to x.

If your kids haven't done any integration, its possible for you to explain it using the average force which the spring will exert when compressing or stretching the spring which will equal 1/2kx. Maybe draw a force vs. time graph of the stretching of a spring to illustrate this.
 

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