The Work to Stretch or Compress a Spring calculator compute the work based on the spring constant (k) and the displacement (x).
INSTRUCTIONS: Choose units and enter the following:
Work on a Spring (W): The calculator returns the work in newton meters (N*m)
The formula for the Work to Stretch or Compress a Spring is:
W = 1/2 k ⋅ x2
defines the force used to displace a spring as: . The minus sign conveys that this is a restorative force acting in opposition to the spring being stretched or compressed.
And then we know that energy is defined to be the ability to do work, so there is a direct relationship between energy and work.
We know that work is force over a distance and in this case the force required to extend (or compress) the spring increases linearly with distance according to our spring-force equation( ). In other words, the more you stretch a spring the harder it gets to stretch it a little farther.
We also know that the work done to compress (or stretch) the spring is equal to the potential energy the spring possesses once the spring is fully extended (compressed) by some distance, x. If we look at the force versus distance graph, we can intuit from out basic knowledge of calculus that the area under the graph of force versus distance is the total work performed. And we can find that area under the graph by integrating the force over the distance x.
So, `W = U = int F*dx = int(k*x*dx) = (1/2) * k*x^2` and this is the total work to compress the spring by a distance, x, and thus is also equivalent to the.
The standard SI units for potential energy are newton-meters which are equivalent to Joules.
Khan Academy'sshows a nice example of applying the potential energy equation for a spring