\u00a9 2023 wikiHow, Inc. All rights reserved. In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distancethat is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. And once we evaluate the fraction, on the right, we find that the value of is 80 newtons per meter. Now, when we sub in the values, we can say that the value of is equal to the force 200 newtons divided by the extension 2.5 meters. Assuming the kinetic energy stays constant (spring-mass is motionless at equilibrium and held in place when stretched), the work done contributes only to increasing the potential energy of the spring-mass system. In Hookes law, the negative sign on the springs force means that the force exerted by the spring opposes the springs displacement. Spring constant is a characteristic of a spring which measures the ratio of the force affecting the spring to the displacement caused by it. Weight is mass times the . Where k is the spring constant, F is the force applied over x, and x is the displacement by the spring expressed in N/m. Each of the blue weights has a mass of 50 grams. When two springs are connected in series, the result is essentially a longer and flimsier spring. Frequency of the resulting SHM. Read on to get a better understanding of the relationship between these values and to learn the spring force equation. Hence, we have a final answer. The natural frequency of a spring-mass system is found to be 2 Hz. Determine the displacement in the spring, the distance by which it is compressed or stretched. Find. What does this mean the spring constant should be? A spring with a 6 N weight added to it stretches by 30 cm relative to its equilibrium position. [A street in Verona. In order to figure out how to calculate the spring constant, we must remember what Hookes law says: Now, we need to rework the equation so that we are calculating for the missing metric, which is the spring constant, or k. Looking only at the magnitudes and therefore omitting the negative sign, you get, The springs used in the shock absorbers must have spring constants of at least 4,900 newtons per meter. Whether it's to pass that big test, qualify for that big promotion or even master that cooking technique; people who rely on dummies, rely on it to learn the critical skills and relevant information necessary for success. An interactive document is an R Markdown file that contains Shiny widgets and outputs. As always, the choice of the positive direction is always ultimately arbitrary (you can set the axes to run in any direction you like, and the physics works in exactly the same way), but in this case, the negative sign is a reminder that the force is a restoring force. They help keep Picture this: you wake up on a Monday morning ready to conquer the week. Answer (1 of 4): ma = -kx (hooke's law) (a = acceleration) From there mv = -(k/2)x^2 As such, v = -(k/2m)x^2 Try this simple exercise - if the force is equal to 60 N, and the length of the spring decreased from 15 to 10 cm, what is the spring constant? This image may not be used by other entities without the express written consent of wikiHow, Inc.
\n<\/p>

\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/d\/de\/Find-Spring-Constant-Step-9.jpg\/v4-460px-Find-Spring-Constant-Step-9.jpg","bigUrl":"\/images\/thumb\/d\/de\/Find-Spring-Constant-Step-9.jpg\/v4-728px-Find-Spring-Constant-Step-9.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"

\u00a9 2023 wikiHow, Inc. All rights reserved. W is the weight of the added mass. Assume that the spring was un-stretched before the body was released. When force is applied to stretch a spring, it can return to its original state once you stop applying the force, just before the elastic limit. T = 2 (m/k). Where, F s F s = Restoring force in spring (N) = Deformation in spring (m) F = Force applied to spring. Dummies helps everyone be more knowledgeable and confident in applying what they know. The variables of the equation are F, which represents force, k, which is called the spring constant and measures how stiff and strong the spring is, and x, the distance the spring is stretched or compressed away from its equilibrium or rest position.\r\n\r\nThe force exerted by a spring is called a restoring force; it always acts to restore the spring toward equilibrium.\r\n\r\nIn Hookes law, the negative sign on the springs force means that the force exerted by the spring opposes the springs displacement.\r\n

Understanding springs and their direction of force

\r\n\r\n

\r\n

The direction of force exerted by a spring

\r\n

\r\nThe preceding figure shows a ball attached to a spring. The formula for Hooke's law specifically relates the change in extension of the spring, x , to the restoring force, F , generated in it: F = kx F = kx. The car designers rush out, ecstatic, but you call after them, Dont forget, you need to at least double that if you actually want your car to be able to handle potholes.","description":"Any physicist knows that if an object applies a force to a spring, then the spring applies an equal and opposite force to the object. You can see that if the spring isnt stretched or compressed, it exerts no force on the ball. Spring-Mass Potential Energy. The spring force is called a restoring force because the force exerted by the spring is always . ","slug":"nuclear-fusion-the-hope-for-our-energy-future","categoryList":["academics-the-arts","science","environmental-science"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/194225"}},{"articleId":184049,"title":"A List of Physics Constants","slug":"a-list-of-physics-constants","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/184049"}},{"articleId":184043,"title":"Physics Equations and Formulas","slug":"physics-equations-and-formulas","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/184043"}},{"articleId":174308,"title":"Calculating Tangential Velocity on a Curve","slug":"calculating-tangential-velocity-on-a-curve","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/174308"}}],"fromCategory":[{"articleId":209405,"title":"String Theory For Dummies Cheat Sheet","slug":"string-theory-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209405"}},{"articleId":209012,"title":"Physics II For Dummies Cheat Sheet","slug":"physics-ii-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/209012"}},{"articleId":208592,"title":"Thermodynamics For Dummies Cheat Sheet","slug":"thermodynamics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208592"}},{"articleId":208578,"title":"Optics For Dummies Cheat Sheet","slug":"optics-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208578"}},{"articleId":208460,"title":"Physics I For Dummies Cheat Sheet","slug":"physics-i-for-dummies-cheat-sheet","categoryList":["academics-the-arts","science","physics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208460"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282467,"slug":"physics-i-for-dummies","isbn":"9781119872221","categoryList":["academics-the-arts","science","physics"],"amazon":{"default":"https://www.amazon.com/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119872227-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119872227/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/9781119872221-203x255.jpg","width":203,"height":255},"title":"Physics I For Dummies","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"

Dr. Steven Holzner has written more than 40 books about physics and programming. How does spring length affect the spring constant? Let's consider the spring constant to be -40 N/m. Recall that Hooke's law states the restoring force is proportional to the spring's displacement. But, if you continue to apply the force beyond the elastic limit, the spring with not return to its original pre-stretched state and will be permanently damaged. References. The formula to calculate the spring constant is as follows: k= -F . Sure, you say. In any situation where you need to calculate the response of an object to a force you use Newton's second law. Mechanical. Since the springs have different spring constants, the displacements are different. Finally, Hookes law assumes an ideal spring. Part of this definition is that the response of the spring is linear, but its also assumed to be massless and frictionless. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. This problem might appear different to the previous examples, but ultimately the process of calculating the spring constant, k, is exactly the same. The spring constant is $250 $ N m$^{-1}$. As long as a spring stays within its elastic limit, you can say that F = kx.

\r\n

When a spring stays within its elastic limit and obeys Hookes law, the spring is called an ideal spring.

\r\n\r\n

How to find the spring constant (example problem)

\r\nSuppose that a group of car designers knocks on your door and asks whether you can help design a suspension system. where F equals force, m equals the mass of the object, and g equals the acceleration due to gravity, 9.8 meters per second2. This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. You know that the force due to the weight of the car is given by F = mg, where g = 9.81 m/s2, the acceleration due to gravity on Earth, so you can adjust the Hookes law formula as follows: However, only one quarter of the total mass of the car is resting on any wheel, so the mass per spring is 1800 kg / 4 = 450 kg. 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. Answer (1 of 2): In simple harmonic motion (no damping), the angular frequency is = (k/m)^0.5, where k is the spring constant and m is the mass of the suspended object. However, after the limit of proportionality for the material in question, the relationship is no longer a straight-line one, and Hookes law ceases to apply. The value of this constant depends on the qualities of the specific spring, and this can be directly derived from the properties of the spring . This mass is displaced 0.7 meters below equilibrium and then launched with an initial velocity of 1 meters/second. Therefore, the spring constant k is the slope of the straight line W versus x plot. The elastic potential energy is equal to the work done (ignoring losses to heat or other wastage), and you can easily calculate it based on the distance the spring has been stretched if you know the spring constant for the spring.