\u00a9 2023 wikiHow, Inc. All rights reserved. It wants the string to come back to its initial position, and so restore it. You can also use it as a spring constant calculator if you already know the force. If you call the equilibrium position of the end of the spring (i.e., its natural position with no forces applied) x = 0, then extending the spring will lead to a positive x, and the force will act in the negative direction (i.e., back towards x = 0). Since the springs have different spring constants, the displacements are different. When a spring stays within its elastic limit and obeys Hooke's law, the spring is called an ideal spring. How to Calculate a Spring Constant Using Hooke's Law. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. When a spring stays within its elastic limit and obeys Hookes law, the spring is called an ideal spring. The spring constant shows how much force is needed to compress or extend a spring (or a piece of elastic material) by a given distance. Th e gray virtual weight hanger has no mass. wikiHow is where trusted research and expert knowledge come together. What does this mean the spring constant should be? The work that must be done to stretch spring a distance x from its equilibrium position is W = kx2. Compare two mass-spring systems, and experiment with spring constant. The work-energy theorem is certainly the easiest way to do the problem, but you can also solve it by calculating the force. Tackling this problem is easy provided you think about the information youve been given and convert the displacement into meters before calculating. k = F x {\displaystyle k= {\frac {F} {x}}} . 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. F is the force and x is the change in spring's length. Assuming these shock absorbers use springs, each one has to support a mass of at least 250 kilograms, which weighs the following:\r\n\r\nF = mg = (250 kg)(9.8 m/s²) = 2,450 N\r\n\r\nwhere F equals force, m equals the mass of the object, and g equals the acceleration due to gravity, 9.8 meters per second². Its as if there is a restoring force in the spring that ensures it returns to its natural, uncompressed and un-extended state after you release the stress youre applying to the material. There are 8 references cited in this article, which can be found at the bottom of the page. The How to Calculate a Spring Constant Using Hooke's Law For a mass attached to a spring, the period of oscillation is equal to 2 (m/k). The formula to calculate the applied force in Hooke's law is: In my case, its seconds^squared vs grams. In short, the spring constant characterizes the elastic properties of the spring in question. The equation for elastic potential energy relates the displacement, x, and the spring constant, k, to the elastic potential PEel, and it takes the same basic form as the equation for kinetic energy: As a form of energy, the units of elastic potential energy are joules (J). He was a contributing editor at PC Magazine and was on the faculty at both MIT and Cornell. In order to figure out how to calculate the spring constant, we must remember what Hookes law says:\r\n\r\nF = kx\r\n\r\nNow, we need to rework the equation so that we are calculating for the missing metric, which is the spring constant, or k. Choose a value of spring constant - for example, 80 N/m. Looking only at the magnitudes and therefore omitting the negative sign, you get\r\n\r\n\r\n\r\nTime to plug in the numbers:\r\n\r\n\r\n\r\nThe springs used in the shock absorbers must have spring constants of at least 4,900 newtons per meter. I actually derived the formula of k = 4^2m/T^2 by differentiating the sin(t) function of displacement twice to find the acceleration, then multiply by mass and divide by amplitude to find spring constant. Imagine that you pull a string to your right, making it stretch. It does. Read on to learn how to apply the formula to find the spring constant, then try your hand with a few practice problems. The force of a spring is calculated using Hookes law, named for Robert Hooke, the 17th-century British physicist who developed the formula in 1660, as he studied springs and elasticity.