The Work Done on a Spring calculator computes the work (W) to further elongate or compress a spring based on the spring constant (k) and the initial and final positions of the spring.
INSTRUCTIONS: Choose units and enter the following:
Work to Elongate or Compress a Spring (W): The calculator returns the work in Newton meters (N•m). However, this can be automatically converted to compatible units (e.g. Joules) via the pull-down menu.
If you integrate the force (F) on spring over a distance, you get the following equation.
`W = int_(x_i)^(x_f) F_x dx = int_(x_i)^(x_f) kx dx = 1/2 kx_2^2 - 1/2 kx_1^2`
where:
This equation is very similar in form to the equation for the potential energy equation.
Work is defined to be the energy transferred by a force and mathematically work is defined in the simplest case where the force is constant to be: Work = Force * Distance.
For example: to move a mass, to just barely get it moving, might require a force of n Newtons. If we continued to apply that force of n Newtons to move the mass some distance, d meters, then he work done would be W = n*d Joules
However, in this case of a force applied to a spring, the force is not constant. The Force is defined to be linearly increasing with the distance, x: `F= k*x`