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Work Done on Spring

vCalc Reviewed
`W = 1/2* k * x_2 ^2-1/2* k * x_1 ^2`
`(k)"Spring Constant"`
`(x_1)"Initial Position"`
`(x_2)"Final position"`
Tags
Physics

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) Spring constant in Newtons per meter (N/m)
  • (x1)  Initial position of Spring
  • (x2)  Final position of 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 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`

Spring Equation Calculators

  • Period of an Oscillating Spring: This computes the period of oscillation of a spring based on the spring constant and mass.
  • Mass of a Spring: This computes the mass based on the spring constant and the period of oscillation. 
  • Angular Frequency of a Spring: This computes the angular frequency based on the spring constant and the mass.
  • Spring Constant: This computes a spring's constant based on the mass and period of oscillation.
  • Work done on a Spring: This computes the work based on the spring constant and the two positions of a spring.
  • Hooke's Law: This computes the force to change the length of a spring based on the spring constant and length of displacement.
  • Force to Fully Compress a Spring: This computes the force required to fully compress a spring based on the spring's physical attributes including the Young's Modulus, wire diameter, length of spring, number of windings, Poisson ratio, and outer diameter of the spring.

References