how to find spring constant with mass how to find spring constant with mass

The spring-mass system can also be used in a wide variety of applications. Example 1 A spring with load 5 Kg is stretched by 40 cm. What does this mean the spring constant should be? A body of mass 0.20 kg is attached to its free end and then released. 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\nThe preceding figure shows a ball attached to a spring. As long as a spring stays within its elastic limit, you can say that F = kx.

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

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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. Meaning, if the material returns to the dimension it had before the load or stress was applied, its deformation is reversible, non-permanent, and it springs back.. What spring constant does the suspension need to have? 1. Find the mass of the block of wood. The negative sign in the equation F = -kx indicates the action of the restoring force in the string. Let's consider the spring constant to be -40 N/m. When a spring stays within its elastic limit and obeys Hookes law, the spring is called an ideal spring.

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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. He has authored Dummies titles including Physics For Dummies and Physics Essentials For Dummies. Dr. Holzner received his PhD at Cornell.

","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8967"}}],"primaryCategoryTaxonomy":{"categoryId":33769,"title":"Physics","slug":"physics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33769"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Understanding springs and their direction of force","target":"#tab1"},{"label":"How to find the spring constant (example problem)","target":"#tab2"}],"relatedArticles":{"fromBook":[{"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"}},{"articleId":194225,"title":"How Does Nuclear Fusion Work? The amount of mechanical energy stored and used by a spring then, is relative to the force and displacementthe harder a spring is pulled, the harder it pulls back. 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. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. He was a contributing editor at PC Magazine and was on the faculty at both MIT and Cornell. Measure the force applied on the spring in Newton (N). The spring constant, k, is the gradient of the straight-line portion of the graph of F vs. x; in other words, force applied vs. displacement from the equilibrium position. 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.","blurb":"","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"

Dr. Steven Holzner has written more than 40 books about physics and programming. 2.4K views . Jennifer holds a JD from Indiana University Maurer School of Law in 2006. Find the spring constant. . How to Calculate a Spring Constant Using Hooke's Law. The spring constant is $250 $ N m$^{-1}$. As the spring mass (ms) is often smaller than the mass (m) of the object, it is generally considered to be = 0 . This problem might appear different to the previous examples, but ultimately the process of calculating the spring constant, k, is exactly the same. What does this mean the spring constant should be?\r\n\r\nIn 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. The mass is 0.4-kilogram and the spring constant is 1.2 Newtons per meter. a. This also means that when you apply the same force to a longer spring as a shorter spring, the longer spring will stretch further than the shorter spring. He was a contributing editor at PC Magazine and was on the faculty at both MIT and Cornell. In other words, if you pull on your length of spring and measure how much force it takes to stretch . If you doubled the length of the spring, on the other hand, its spring constant would be half what it was. wikiHow, Inc. is the copyright holder of this image under U.S. and international copyright laws. The Period of a Mass-Spring System calculator computes the period () of a mass-spring system based on the spring constant and the mass. In F = -kx, x is the compression or stretch of the spring, so at first the force on the mass is F = k*0.035 = 0.84 N as you found. 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. 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 Variables in Hooke's Law Equation. K = - F s F s Or K = F F . 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. To the right? Sure, you say. 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.. Weight is mass times the . He has authored Dummies titles including Physics For Dummies and Physics Essentials For Dummies. Dr. Holzner received his PhD at Cornell.

","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"

Dr. Steven Holzner has written more than 40 books about physics and programming. As a formula, it reworks Hooke's Law . How strong do the springs have to be? 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 if needed. Whether you need help solving quadratic equations, inspiration for the upcoming science fair or the latest update on a major storm, Sciencing is here to help. It is different for different springs and materials. The minus sign shows that this force is in the opposite direction of the force thats stretching or compressing the spring. The mass of the carts themselves, without the masses on top of them, is 500 grams. Solution: Given: Mass m = 5 Kg. 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.","blurb":"","authors":[{"authorId":8967,"name":"Steven Holzner","slug":"steven-holzner","description":"

Dr. Steven Holzner has written more than 40 books about physics and programming. The good news its a simple law, describing a linear relationship and having the form of a basic straight-line equation. A good example of SHM is an object with mass m attached to a spring on a frictionless surface, as shown in Figure 15.3. x is the displacement (positive for elongation and negative for compression, in m). Thank you very much for your cooperation. He was also a science blogger for Elements Behavioral Health's blog network for five years. F is the force and x is the change in spring's length. Its important to stress again that Hookes law doesnt apply to every situation, and to use it effectively youll need to remember the limitations of the law. Solution: 1.Find out the force applied on the spring. The gravitational force, or weight of the mass m acts downward and has magnitude mg, We use cookies to make wikiHow great. The size of the relationship between the extension and the restoring force of the spring is encapsulated in the value the spring constant, k. 1. Determine the displacement in the spring, the distance by which it is compressed or stretched. It always has a positive value. The spring constant tells you how much force the spring exerts when it does that, but how do you figure out what the spring constant is? Use this information to find the spring constant (use g = 9.81 m/s as the acceleration of gravity). A mass on a spring has a single resonant frequency determined by its spring constant k and the mass m. Using Hooke's law and neglecting damping and the mass of the spring, Newton's second law gives the equation of motion: . By entering your email address and clicking the Submit button, you agree to the Terms of Use and Privacy Policy & to receive electronic communications from Dummies.com, which may include marketing promotions, news and updates. The force resists the displacement and has a direction opposite to it, hence the minus sign. Read on to get a better understanding of the relationship between these values and to learn the spring force equation. Thus we get three equations: First equate equations 2 and 3 and . We created the Hooke's law calculator (spring force calculator) to help you determine the force in any spring that is stretched or compressed. N/m * m = N. You can also use the Hooke's law calculator in advanced mode, inserting the initial and final length of the spring instead of the displacement. If you push the spring, however, it pushes back, and if you pull the spring, it pulls back.\r\n

Hookes law is valid as long as the elastic material youre dealing with stays elastic that is, it stays within its . If you pull a spring too far, it loses its stretchy ability. Plug the values for the second weight into the formula to find the spring constant: [11] The formula to find the spring constant is. This image may not be used by other entities without the express written consent of wikiHow, Inc.
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\n<\/p><\/div>"}. You can use Hooke's law calculator to find the spring constant, too. Displacement x=20cm. k = 588 The previous mass is detached from the spring and a mass of 14 kilograms is attached. When you compress or extend a spring or any elastic material youll instinctively know whats going to happen when you release the force youre applying: The spring or material will return to its original length. The spring force formula is expressed through the equation: F = kx. In order to figure out . The second is measuring period squared (T^2) vs mass. The block of wood experiences a maximum speed of 25 m / s. Find the value of the spring constant. Now you simply have to input the known values and solve to find the strength of the springs needed, noting that the maximum compression, 0.1 m is the value for x youll need to use: This could also be expressed as 44.145 kN/m, where kN means kilonewton or thousands of newtons.. Did you know? Thank you very much for your cooperation. This image is not<\/b> licensed under the Creative Commons license applied to text content and some other images posted to the wikiHow website. The springs wide use and application are due to its ability to store mechanical energy. 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). 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. Ignoring the minus sign in Hookes law (since the direction doesnt matter for calculating the value of the spring constant) and dividing by the displacement, x, gives: Using the elastic potential energy formula is a similarly straightforward process, but it doesnt lend itself as well to a simple experiment. In order to continue enjoying our site, we ask that you confirm your identity as a human. Thanks to all authors for creating a page that has been read 6,469 times. The apparatus setup shown in fig. Knowing that BT . A higher spring constant means a stiffer spring thats harder to stretch (because for a given displacement, x, the resulting force F will be higher), while a looser spring thats easier to stretch will have a lower spring constant. He has authored Dummies titles including Physics For Dummies and Physics Essentials For Dummies. Find the equation of motion. Read on to learn how to apply the formula to find the spring constant, then try your hand with a few practice problems. 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Dr. Steven Holzner has written more than 40 books about physics and programming. Snapshots of the lab are found in the four figures that follow. You can also use it as a spring constant calculator if you already know the force. The spring constant, k, is a measure of the stiffness of the spring. This image may not be used by other entities without the express written consent of wikiHow, Inc.
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