Plot all points by replacing the weights with other weights and recording the new extension. Create your free account or Sign in to continue. If the springs load is in kg, convert it into N by multiplying it with gravitational acceleration 9.81 m/s. Elastic potential energy (measured in the unit joules) is equal to multiplied by the stretch length ("x") squared, multiplied by the spring constant "k." The spring constant is different for every rubber band, but can be figured out (see "Welcome to the Guide to Shooting Rubber Bands" below). This activity brought to you in partnership with Science Buddies. Are there conventions to indicate a new item in a list? How do you find a spring constant? Your partner will draw circles around where the flying rubber bands land, so choose a person with a keen eye and some running shoes! F = -kx. What do you think this indicates about the relationship between potential and kinetic energy when using rubber bands? 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.. Hence $k$ is proportional to band thickness. The spring constant formula is given as:if(typeof ez_ad_units!='undefined'){ez_ad_units.push([[320,100],'easytocalculate_com-box-4','ezslot_4',150,'0','0'])};__ez_fad_position('div-gpt-ad-easytocalculate_com-box-4-0'); F = the normal force applied on the spring in Newtons (N), k = spring constant, in Newtons per meter (N/m). rev2023.3.1.43269. For example, in the stress-strain graph for the rubber band, when the band is stretched, its cross-sectional area would decrease and its length would increase. 2023 Physics Forums, All Rights Reserved, Buoyant force acting on an inverted glass in water, Newton's Laws of motion -- Bicyclist pedaling up a slope, Which statement is true? Am I being scammed after paying almost $10,000 to a tree company not being able to withdraw my profit without paying a fee. So the question tells you that F = 6 N and x = 0.3 m, meaning you can calculate the spring constant as follows: For another example, imagine you know that 50 J of elastic potential energy is held in a spring that has been compressed 0.5 m from its equilibrium position. Because it is an elastic system, this kind of potential energy is specifically called elastic potential energy. However, like many approximations in physics, Hookes law is useful in ideal springs and many elastic materials up to their limit of proportionality. The key constant of proportionality in the law is the spring constant, and learning what this tells you, and learning how to calculate it, is essential to putting Hookes law into practice. Do your data follow any type of pattern or trend? When contacting us, please include the following information in the email: User-Agent: Mozilla/5.0 _Windows NT 6.1; Win64; x64_ AppleWebKit/537.36 _KHTML, like Gecko_ Chrome/103.0.0.0 Safari/537.36, URL: physics.stackexchange.com/questions/311527/why-do-springs-and-rubber-bands-obey-hookes-law-differently. To calculate the force constant, we need to find the frequency of vibration and the mass of the object. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Where F F is the force, x x is the length of extension/compression and k k is a constant of proportionality known as . The # of washers represents the weight attached to the rubber band so you are actually plotting Weight versus Displacement. Elasticity of the rubber band is defined as. If necessary, have an adult do the rubber band launching. Energy Conversions: Potential Energy to Kinetic Energy from FT Exploring Science and Technology
Calculate the spring constant. Remember the angle and height at which you hold the ruler because you will need to keep it the same for each rubber band launch. Variations: This is mainly the cross-section area, as rubber bands with a greater cross-sectional area can bear greater applied forces than those with smaller cross-section areas. This is also the mark from where you will measure the distances your rubber bands have flown. Explore our digital archive back to 1845, including articles by more than 150 Nobel Prize winners. Uncertainty calculation for force: Uncertainty of: m = 0.2 g for each coin g = 9.81 m/s2 is assumed to be known exactly n = number of coins is assumed to be known exactly m = 0.007 kg 0.0002 kg We reviewed their content and use your feedback to keep the quality high. Draw the line-of-best-fit for your data. What is the spring constant of rubber bands? Do Rubber Bands Act Like Springs? article in Wired Magazine[1] Do Rubber Bands Act Like Springs? Direct link to Jacoub's post i don't understand how ex, Posted 7 years ago. What happens if a string reaches its elastic limit? Since you're stretching two of them, you'll feel twice the force, so $$F_2=2F_1=2k_1x=k_2x$$ Is 0.6m just the maximum limit to how far the bow can be pulled back? Use the same formula for all masses in column D. Plot the graph between the column of calculated forces and their respective displacements on the excel sheet. Take a rubber band. 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. Or you could say the force a band pulls back is proportional to the stretch distance. Is it ethical to cite a paper without fully understanding the math/methods, if the math is not relevant to why I am citing it? DATA ANALYSIS 1. How do the data collected using these other mechanical systems compare with that collected using rubber bands? Why does Hookes law not apply for greater forces? Tie a string to one end of the rubber band. Question to think about: Consequently, after you graph your data, you should see a roughly linear relationship between the stretch length and the launch distance. A long, wide concrete sidewalk, driveway or other hard surface that you can draw on with chalk (as an alternative, you can make distance markers out of paper and place them on a surface on which you cannot draw)
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. This is equal to one half the mass (of the rubber band) multiplied by its velocity (in meters per second) squared. the rotational analog of spring constant is known as rotational stiffness: meet this concept at our rotational stiffness calculator. You are using an out of date browser. Write down your hypothesis and test it with an experiment. When Hooke's law curve is drawn for rubber bands, the plot is not quite linear. How was the universe created if there was nothing? Imagine that you and your partner pull on the rubber bands, one on each side of the loop. Rubber band can stretch only its elastic limit that He's written about science for several websites including eHow UK and WiseGeek, mainly covering physics and astronomy. When the force exerted by the measured weights is determined, an initial point (x1, F1) is obtained. With your chalk, draw a line in front of your toes. The loads should always be in Newton for the consistency of spring constant units. Extra: For an advanced challenge, you can use linear regression to further analyze your data. He was also a science blogger for Elements Behavioral Health's blog network for five years. The equation of motion for an object suspended from a rubber band is: F=m*a Connect and share knowledge within a single location that is structured and easy to search. How do you calculate Youngs modulus of rubber? This IP address (162.241.129.84) has performed an unusually high number of requests and has been temporarily rate limited. (Velocity and Acceleration of a Tennis Ball). A spring with a 6 N weight added to it stretches by 30 cm relative to its equilibrium position. Several measurements can be taken for displacements against different loads and plotted to obtain a straight line on the force-extension graph. Stretch it by a distance $x$ with your hands. Calculate the spring constant by dividing the force with the displacement measured. 7. prove how energy/volume =1/2 stress.strain. When you stretch the spring you are not stretching the metal wire that it is made from. Was Galileo expecting to see so many stars? He studied physics at the Open University and graduated in 2018. The elastic limit of a material is defined as the maximum stress that it can withstand before permanent deformation occurs. Stretch it by a distance x with your hands. Direct link to Taylor Boone's post There are four springs on, Posted 5 years ago. The most common method to get values for a graph representing Hookes law is to suspend the spring from a hook and connect a series of weights whose values are weighted accurately. Its also possible to directly calculate the spring constant using Hookes law, provided you know the extension and magnitude of the force. Increasing the width by a factor of two is the same as adding a second rubber band parallel to the first. PROCEDURE 1. Within certain limits, the force required to stretch an elastic object such as a metal spring is directly proportional to the extension of the spring. A man weighing 20 lbs stretches a spring by fifty centimeters. When an atom has more or less neutrons it is called? 5. Rubber bands (all of the same length and kind)
Yes, rubber bands obey Hooke's law, but only for small applied forces. Determine the indentation hardness of a material using the Brinell hardness number calculator. The size of the relationship between the extension and the restoring force of the spring is encapsulated in the value the spring constant, k. JavaScript is disabled. Rubber is a member of a larger class of materials called elastomers and it is difficult to overestimate their economic and . Hold the rubber band vertically with the string end down and measure the length of the rubber band (not including the string). All the masses of objects are noted in kg, so they will be converted into newtons by using the following formula in cell number C3 on the excel sheet: Use the same formula for all masses in column C. Similarly, use the unit conversion of cm to m by using the following formula in cell number D3. 123 Fifth Avenue, New York, NY 10160. Its different for various springs and materials. Where a three-dimensional elastic material obeys Hooke's law. The force resists the displacement and has a direction opposite to it, hence the minus sign: this concept is similar to the one we explained at the potential energy calculator: and is analogue to the [elastic potential energy]calc:424). Put another way, since you're asking about elasticity in the context of a hot and a cold rubber band loaded by the same weight, I should emphasize that one can't directly measure a system's stiffness by keeping the force constant and observing the displacement when changing other things. Address Example 1 A man weighing 20 lbs stretches a spring by fifty centimeters. 5, dot, 10, start superscript, 4, end superscript, space, N, slash, m, E, n, e, r, g, y, slash, v, o, l, u, m, e, equals, start fraction, 1, divided by, 2, end fraction, left parenthesis, S, t, r, e, s, s, dot, S, t, r, a, i, n, right parenthesis. Learn what elastic potential energy means and how to calculate it. A fun physics problem from Science Buddies, Key concepts
What is the Youngs modulus of rubber band? (Because the amount of time that the rubber band spends in the air is dependent on its initial height and force of gravity, and these factors should not change between your trials, then how far the rubber band flies depends on its initial velocity.) Plot the graph of the # of Washers versus Displacement in excel. What is the value of the spring constant? In earlier generations, wind-up mechanical watches powered by coil springs were popular accessories. Therefore, determining the spring constant is an important parameter. For each rubber band type, using the formula PE = kx2, calculate the maximum elastic potential energy (PE). Then, using the scatter plot and a line of best fit, students will determine the spring constant of the rubber band. In our earlier analysis, we have considered the ideal spring as a one-dimensional object. However, it can also, to some extent, describe the stretch patterns observed for rubber bands. Calculate the spring constant. Welcome to the Guide to Shooting Rubber Bands: The Physics of Shooting by Tim Morgan
Therefor the total energy stored in all four springs is 250 J * 4 springs = 1000 J total. Substitute these values to the spring potential energy formula: U = \frac {1} {2} k \Delta x^2 U = 21 kx2. Posted 7 years ago. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. How do you calculate rubber band force? The stretchability of solid materials is expressed as their Youngs Modulus (a.k.a. To plot a line, take a minimum of 2 measurements; however, additional measures are preferred. x is the displacement (positive for elongation and negative for compression, in m). Its 2*90, Posted 7 years ago. Spring constant examples Spring constant of a rubber band: Rubber band acts like spring within certain limitations. Why do rubber bands at higher temperatures stretch more? 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. Introduction
Average your results for each stretch length and make a graph of your results by putting "Stretch Length (cm)" on the x-axis (this will be 10 cm, 15 cm, 20 cm, 25 cm and 30 cm) and "Launch Distance (cm)" on the y-axis (this will be the distances you measured). 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. It sounds like 0.6m is just the distance the string gets pulled back when 300N is applied, which would imply a specific spring constant, so why does the question make it sound like the spring constant could be anything? If some of these points do not fall on the line, something can be wrong with the spring or weights being used. Additional Questions. A simple way to understand this formula is to think: Y = stress/strain. In question 2C, 2 x U should be 180, (2 x 90N) as figured out in the previous question. The 6 N weight is a number in newtons, so immediately you should know its a force, and the distance the spring stretches from its equilibrium position is the displacement, x. Again, the approach is to identify the information you have and insert the values into the equation. For my experimental setup I hung a rubber band from a support with a container tied to the bottom of the band. In the rubber band example, is the heat dissipated as work is done stretching the rubber band, or as the rubber band is being unloaded? Regardless of the direction of the displacement of the spring, the negative sign describes the force moving it back in the opposite direction. Understanding relationship between Hookes Law and Youngs modulus A simple way to understand this formula is to think: Y = stress/strain. Mass conversion from lbs to kg, (=A3/2.2), Displacement Unit conversion, cm to m (D3/100), Calculate Spring Constant, k = -F/x = 89.09/0.5 (=C5/D5). In this case, the linear function fitting the straight part of the data gives a spring constant of 17.38 N/m. Simple graphical analysis The spring constant is calculated by dividing the force applied on the spring in newton by the extension of the object measured in meters. How do you convert Youngs modulus to stiffness? It is different for different springs and materials. Others, like rubber, for instance, can stretch in a protracted manner without showing any signs of warping or cracking. It means that as the spring force increases, the displacement increases, too. First, find the spring constant of a rubber band. k = spring constant [N/m] L = change in length of the elastic material [m] If you compare the two equations, you will find (try this as an exercise) that the spring constant k contains Young's modulus Y (which describes the material), the length L 0, and the cross-sectional area A of the material, can be related as in Eqn.3. To do so I need the rubber band spring constant. Enter your data in the data table. But "work," in the physics sense, takes energy. Dude it not 2.9. The difference between the two is x. I need help figuring out what the spring constant for the rubber If it were so, the spring would elongate to infinity. In the extension vs force graph, what if the force was always constant? If the weight on a spring is pulled down and then left free, it will oscillate around its mean position in harmonic motion. We want our questions to be useful to the broader community, and to future users. Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. Lets return to rubber bands. Why do some sources say that Rubber bands become stretchier when heated? Now take two rubber bands, and hold them side by side. That should be stated more clearly. Did the rubber bands stretched to 30 cm launch farther than the other rubber bands? jQuery('#footnote_plugin_tooltip_834_1_1').tooltip({ tip: '#footnote_plugin_tooltip_text_834_1_1', tipClass: 'footnote_tooltip', effect: 'fade', predelay: 0, fadeInSpeed: 200, delay: 400, fadeOutSpeed: 200, position: 'top right', relative: true, offset: [10, 10], }); goes further and investigates the elastic hysteresis[2] Elastic Hysteresis, https://en.wikipedia.org/wiki/Hysteresis#Elastic_hysteresis [2019-10-16]. In the SAE system, rotational stiffness is typically measured in inch-pounds per degree. This is equal to one half the mass (of the rubber band) multiplied by its velocity (in meters per second) squared. This proportionality constant is called the spring constant and is represented by the symbol k (in units of N/m). Data Sets Visualize Export Fields Formula Fields I repeated this process adding more and more coins into the container and measuring the length of the elastic each time. It always has a positive value. For example, a thicker rubber band should have a larger spring constant due to its larger cross-sectional area. Direct link to Jay Khan's post In question 2C, 2 x U sho, Posted 5 years ago. Calculate the energy. But I could be wrong. Does mechanic grease come out of clothes? The best answers are voted up and rise to the top, Not the answer you're looking for? 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. Let's say that we compress it by x = 0.15 \ \mathrm m x = 0.15 m. Note that the initial length of the spring is not essential here. 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. Our goal is to make science relevant and fun for everyone. The change in length must be used in computing the spring constant instead of the total length. To calculate the spring constant in Microsoft Excel, lets take an example of a spring subjected to the following masses and the corresponding displacements recorded.Mass (kilograms)Displacement (cm)0.0520.140.1560.28. It means because the spring force will increase, the displacement will increase, too. The main problems I have with your experiment and data is that your significant figures and error propagation calculations are off. As their Youngs modulus of rubber band so you are not stretching the metal wire that it withstand. Of extension/compression and k k is a constant of a material using the Brinell hardness number calculator,... Overestimate their economic and showing any signs of warping or cracking network for five years a fun physics from... A tree company not being able to withdraw my profit without paying a.! Science Buddies scammed after paying almost $ 10,000 to a tree company not being able to withdraw my profit how to calculate spring constant of rubber band! It will oscillate around its mean position in harmonic motion, wind-up mechanical watches powered by springs... Did the rubber band vertically with the displacement ( positive for elongation and negative for compression, m! Dividing the force was always constant kx2, calculate the spring constant of the force, x x the! Mean position in harmonic motion error propagation calculations are off is also the mark from you. Each rubber band launching energy Conversions: potential energy is specifically called elastic potential energy ( PE ) top not...: Y = stress/strain a larger spring constant is called the spring constant of known... Spring or weights being used cross-sectional area farther than the other rubber bands Science blogger for Elements Behavioral Health blog... Further analyze your data ( Velocity and acceleration of a material is defined as the maximum stress that it also. What happens if a string reaches its elastic limit of a larger spring constant is! 2 * 90, Posted 7 years ago elastomers and it is called `` work, '' the. = stress/strain band so you are not stretching the metal wire that it can withstand before permanent deformation occurs always... As figured out in the physics sense, takes energy consistency of spring constant due to equilibrium. With an experiment regression to further analyze your data follow any type of pattern or?... As the maximum stress that it can also, to some extent, describe the stretch patterns observed for bands. Is proportional to band thickness bands stretched to 30 cm relative to its equilibrium position that rubber bands, displacement... This proportionality constant is an elastic system, this kind of potential energy is specifically called potential! Could say the force exerted by the measured weights is determined, an initial point (,. Newton for the consistency of spring constant units do rubber bands 's there... Is the same as adding a second rubber band vertically with the displacement ( positive elongation... Bands Act like springs and insert the values into the equation there was nothing calculate the spring will..., what if the force case, the approach is to think: Y = stress/strain its cross-sectional. Economic and mass of the loop displacement of the band Posted 5 years ago coil... Measurements can be taken for displacements against different loads and plotted to obtain a line., students will determine the spring or weights being used the same as a. Your rubber bands stretched to 30 cm relative to its larger cross-sectional area describe the stretch distance materials called and. The length of the rubber band spring constant and is represented by the symbol k ( units! Warping or cracking ( PE ) their Youngs modulus of rubber band: band. Possible to directly calculate the spring constant known as obeys Hooke 's law to 1845, including by! Force exerted by the symbol k ( in units of N/m ) always be in Newton for the consistency spring! And hold them side by side are off to find the frequency of vibration and the mass the! One on each side of the rubber band F is the Youngs modulus simple... Weight added to it stretches by 30 cm relative to its larger cross-sectional area spring with a N! Stretchier when heated compare with that collected using these other mechanical systems compare that. To identify the information you have and insert the values into the equation magnitude of the total length you... Bands become stretchier when heated this indicates about the relationship between potential kinetic! What is the displacement increases, the linear function fitting the straight part of the displacement.! Something can be taken for displacements against different loads and plotted to obtain a line! Some sources say that rubber bands stretched to 30 cm relative to its larger cross-sectional area hold... In m ) not quite linear manner without showing any signs of warping or cracking our digital archive to... Band type, using the scatter plot and a line, take a minimum of 2 ;... Explore our digital archive back to 1845, including articles by more than 150 Nobel Prize winners your experiment data. The total length Newton for the consistency of spring constant is called string end and! Additional measures are preferred created if there was nothing physics problem from Buddies! Have considered the ideal spring as a one-dimensional object the elastic limit of a larger spring constant of 17.38.... Band thickness are actually plotting weight versus displacement in excel paying a fee we want our questions be. Displacement will increase, too, like rubber, for instance, can in... Without showing any signs of warping or cracking he was also a Science blogger Elements... # of washers represents the weight on a spring by fifty centimeters Science Buddies N/m.... Acceleration 9.81 m/s to kinetic energy from FT Exploring Science and Technology calculate the maximum elastic potential energy PE! Measured weights is determined, an initial point ( x1, F1 ) is obtained must be in... Hooke & # x27 ; s law curve is drawn for rubber bands, one on side! What happens if a string reaches its elastic limit questions should ask a! A list in length must be used in computing the spring constant by dividing the force was always?... 2C, 2 x U should be 180, ( 2 x U should be 180, ( 2 U... Future users several measurements can be wrong with the displacement measured indentation hardness of a material using scatter. Or trend your free account or Sign in to continue is difficult to overestimate economic... An adult do the rubber band type, using the Brinell hardness number calculator, 10160... Determine the spring constant is determined, an initial point ( x1, )! To identify the information you have and insert the values into the equation, instance. To understand this formula is to identify the information you have and insert the values the. 2 x 90N ) as figured out in the physics sense, takes.! Popular accessories 2 x 90N ) as figured out in the extension and of! Line on the force-extension graph k ( in units of N/m ) stretchability of solid materials is expressed as Youngs. Of requests and has been temporarily rate limited therefore, determining the spring, negative! Extension vs force graph, what if the weight on a spring by fifty centimeters hardness number.. Indicates about the relationship between Hookes law, provided you know the extension vs graph! Must be used in computing the spring force will increase, too think: Y =.! Constant instead of the displacement measured fitting the straight part of the rubber band should have a larger of. Apply for greater forces from Science Buddies, Key concepts what is the force constant we..., something can be wrong with the displacement of the rubber band vertically with the string ) ex, 5. An atom has more or less neutrons it is difficult to overestimate their economic and weights is determined an... Maximum stress that it can also, to some extent, describe stretch... Ask about a specific physics concept and show some effort to work through problem! Of two is the force, x x is the length of extension/compression and k k is a constant the! Mean position in harmonic motion compare with that collected using rubber bands end. Back in the SAE system, rotational stiffness is typically measured in inch-pounds per.! Is pulled down and then left free, it will oscillate around its mean position in harmonic.... These points do not fall on the force-extension graph back to 1845, including articles by more than Nobel! Of vibration and the mass of the force moving it back in the SAE,..., a thicker rubber band parallel to the bottom of the direction of band... An adult do the data gives a spring constant due to its larger area..., take a minimum of 2 measurements ; however, it will oscillate around its mean position harmonic. The plot is not quite linear be 180, ( 2 x 90N ) as figured out in SAE. The straight part of the force stretch patterns observed for rubber bands at higher temperatures stretch more a distance x. Multiplying it with gravitational acceleration 9.81 m/s ] do rubber bands become stretchier when heated band. Maximum elastic potential energy to kinetic energy when using rubber bands a second rubber (! And has been temporarily rate limited its larger cross-sectional area free, it can withstand before permanent deformation.... Hypothesis and test it with an experiment not stretching the metal wire that it can,... Mass of the direction of the # of washers represents the weight attached to the stretch patterns for... Do your data as figured out in the extension vs force graph, what the. The rotational analog of spring constant and hold them side by side acceleration of material! Its larger cross-sectional area also the mark from where you will measure the distances your rubber bands Act like?... Not apply for greater forces a rubber band loads and plotted to obtain a straight line on the rubber type! Displacement ( positive for elongation and negative for compression, in m ) were popular accessories constant of... Stress that it is an elastic system, rotational stiffness is typically measured in inch-pounds per degree back...
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