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Calculate the Spring Force
As discussed in Halliday and Resnick's "Fundamentals of Physcis," Hooke's law states that the formula relating the force a spring exerts, as a function of its displacement from its equilibrium length, is force F = -kx. x here is a measure of the displacement of the free end of the spring from its unloaded, unstressed position. k is a proportionality constant called the "stiffness," and is specific to each spring. The minus sign is in front because the force that the spring exerts is a "returning" force, meaning that it opposes the direction of displacement x, in an effort to return the spring to its unloaded position. The spring equation usually holds for displacement x in both directions--both stretching and compressing displacement--although there can be exceptions. If you don't know k for a specific spring, you can calibrate your spring using a weight of known mass.
Instructions
1.Determine the position of the free end of the spring, if hanging loosely--its other end affixed to something solid like a wall.
2.Decide what displacement x from the equilibrium position you want to know the spring force, measuring it in meters.
3.Multiply x by -k to find the force that the spring exerts to try to return to its equilibrium position. If x is in meters and k is in kilograms per second-squared, then force F is in Newtons, the SI unit for force.
4.If you don't know k, proceed to the next step to determine it.
5.Find the spring's proportionality constant k by hanging a weight of known mass m, preferably in kilograms, from the free end of the spring, after positioning it vertically. From the resulting displacement, you can determine k by the relation k = -mg/x, where g is the gravitational acceleration constant 9.80m/s^2, where the caret ^ indicates exponentiation.