\u00a9 2023 wikiHow, Inc. All rights reserved. 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 find the spring constant, we first need to find the force that is acting on the spring. A force of 16 N is required to stretch a spring a distance of 40 . 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 mass is 0.4-kilogram and the spring constant is 1.2 Newtons per meter. Thus we get three equations: First equate equations 2 and 3 and . The spring force is called a restoring force because the force exerted by the spring is always . He was a contributing editor at PC Magazine and was on the faculty at both MIT and Cornell. When a spring stays within its elastic limit and obeys Hookes law, the spring is called an ideal spring. He was also a science blogger for Elements Behavioral Health's blog network for five years. He was a contributing editor at PC Magazine and was on the faculty at both MIT and Cornell. gives the force a spring exerts on an object attached to it with the following equation:\r\n\r\nF = kx\r\n\r\nThe minus sign shows that this force is in the opposite direction of the force thats stretching or compressing the spring. 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. The unloaded length of a spring is measured. 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. spring-mass system. F is the force and x is the change in spring's length. You find the spring constant by suspending weights from the spring, recording the extensions and plotting a graph. a. Knowing that BT . What is the spring constant k for the spring? The spring constant of a spring can be found by carrying out an experiment. The only other forces exerted on the mass are . I draw line of best fit and determine the slope. References. Where F is the force exerted on the spring in Newtons (N),. 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 This limit depends on its physical properties. A mass-spring system oscillates with an amplitude of 3.5 cm. . The frequency of the vibration is f = /2. Tackling this problem is easy provided you think about the information youve been given and convert the displacement into meters before calculating. How far below the initial position the body descends, and the. They inform you that the car will have a mass of 1,000 kilograms, and you have four shock absorbers, each 0.5 meters long, to work with. A springs elasticity will return to its original form once the outside force, whatever the mass, is removed. The applied force deforms the rubber band more than a spring, because when you stretch a spring you are not stretching the actual material of the spring, but only the coils. The block of wood experiences a maximum speed of 25 m / s. Find the value of the spring constant. Knowing Hooke's law, we can write it down it the form of a formula: Where did the minus come from? What is the spring constant in this case? \begin{aligned} k&=\frac{F}{x} \\ &= \frac{6\;\text{N}}{0.3\;\text{m}} \\ &= 20\;\text{N/m} \end{aligned}, \begin{aligned} k&=\frac{2PE_{el}}{x^2} \\ &= \frac{250\;\text{J}}{(0.5\;\text{m})^2} \\ &=\frac{100\;\text{J}}{0.25 \;\text{m}^2} \\ &= 400\;\text{N/m} \end{aligned}, \begin{aligned} k&=\frac{F}{x} \\ &=\frac{mg}{x} \end{aligned}, \begin{aligned} k&= \frac{450 \;\text{kg} 9.81 \;\text{m/s}^2}{0.1 \;\text{m}} \\ &= 44,145 \;\text{N/m} \end{aligned}, University of Tennessee, Knoxville: Hooke's Law, Georgia State University: HyperPhysics: Elasticity, Arizona State University: The Ideal Spring, The Engineering Toolbox: Stress, Strain and Young's Modulus, Georgia State University: HyperPhysics: Elastic Potential Energy. The displacement of an object is a distance measurement . Last Updated: February 20, 2023 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 equation can also be stated: F = k x. 0.035 m {\displaystyle 0.035m} You can also use it as a spring constant calculator if you already know the force. Of course, the spring doesnt have to move in the x direction (you could equally well write Hookes law with y or z in its place), but in most cases, problems involving the law are in one dimension, and this is called x for convenience. However, in many cases especially in introductory physics classes youll simply be given a value for the spring constant so you can go ahead and solve the problem at hand. The spring constant is determined using the value of the force applied and the displacement caused by Force on the spring. Recall that Hooke's law states the restoring force is proportional to the spring's displacement. 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. As you make your morning coffee, your dog starts whimpering and you realize theyre unwell. Spring-Mass Potential Energy. If it were so, the spring would elongate to infinity. In Hookes law, the negative sign on the springs force means that the force exerted by the spring opposes the springs displacement. Springs with larger spring constants will have smaller displacements than springs with lesser spring constants for the same mass added. 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\/0\/05\/Find-Spring-Constant-Step-8.jpg\/v4-460px-Find-Spring-Constant-Step-8.jpg","bigUrl":"\/images\/thumb\/0\/05\/Find-Spring-Constant-Step-8.jpg\/v4-728px-Find-Spring-Constant-Step-8.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"