# Work Done on Spring

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vCalc.Work Done on Spring
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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:

• (k) This is the spring constant in Newtons per meter (N/m)
• (x1)  This is the initial position of the spring.
• (x2)  This is the final position of the spring

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.

#### The Math / Science

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:

• k is the spring constant
• xi is the initial position of the spring
• xf is the final position of the spring

This equation is very similar in form to the equation for the potential energy of the spring and is often confused with 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

Khan Academy's Introduction to work and energy