how to calculate spring constant of rubber band
k = F / (1). the rotational analog of spring constant is known as rotational stiffness: meet this concept at our rotational stiffness calculator. 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. 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. Measure how far you stretched the rubber band with a ruler and record the length, in meters (m), as your displacement ( x ) Release the rubber band and record how far it travels in meters.. 10. Rubber Bands for Energy from Science Buddies 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) Discover world-changing science. This is equal to one half the mass (of the rubber band) multiplied by its velocity (in meters per second) squared. Does With(NoLock) help with query performance? 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. Objects of given weight (granola bars, packaged foods, etc.) Was Galileo expecting to see so many stars? Why do rubber bands not follow Hookes Law? 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. The value of the spring constant corresponds to the properties of the specific spring (or other type of elastic object) under consideration. Hookes law is a fondamental rule of thumb applied on skin that describes a direct proportionality link between the force applied on an object and the induced strain. Try this simple exercise - if the force is equal to 60N60\ \mathrm{N}60N, and the length of the spring decreased from 15cm15\ \mathrm{cm}15cm to 10cm10\ \mathrm{cm}10cm, what is the spring constant? The dot there is for multiplication, Why in Exercise1 250J/spring = 1000J? This IP address (162.241.129.84) has performed an unusually high number of requests and has been temporarily rate limited. Choose a value of spring constant - for example. Rubber elasticity refers to a property of crosslinked rubber: it can be stretched by up to a factor of 10 from its original length and, when released, returns very nearly to its original length. Recalculate it without rounding ( I could have put the values in my calculator wrong, so if you get the same value maybe it's me who made the mistake!). As it is stretched (loaded), the curve takes the upper path. The spring constant is a key part of Hookes law, so to understand the constant, you first need to know what Hookes law is and what it says. Lee Johnson is a freelance writer and science enthusiast, with a passion for distilling complex concepts into simple, digestible language. from Wisconsin K-12 Energy Education Program (KEEP) Metric ruler You can use Hooke's law calculator to find the spring constant, too. https://www.wired.com/2012/08/do-rubber-bands-act-like-springs/[2019-10-16]. What do you think this indicates about the relationship between potential and kinetic energy when using rubber bands? What does the slope of the line-of-best-fit for # of washers versus displacement tell you about the rubber band? Small metal hanger Use items of known mass to provide the applied force. Since you're stretching two of them, you'll feel twice the force, so. This limit depends on its physical properties. How do you convert Youngs modulus to stiffness? For example, a thicker rubber band should have a larger spring constant due to its larger cross-sectional area. 3. An object designed to store elastic potential energy will typically have a high elastic limit, however all elastic objects have a limit to the load they can sustain. The Hold the rubber band vertically with the string end down and measure the length of the rubber band (not including the string). The energy transferred to a spring's elastic store is given by the equation: \(Ee = \frac{1}{2} \: k \: x^{2}\) Compare the area under the line, from the origin up to a point, with the calculation . Several measurements can be taken for displacements against different loads and plotted to obtain a straight line on the force-extension graph. Ruler (30cm) or flexible tape measure. B D E F. G H T Displacemerl Washers 0.006 0.009 Washers 0.011 14 4 y = 219.72x + 0.9338" 0.014 0.016 0.02 12 10 RRE 0 von WNP 8 9 6 0.023 0.027 0.034 0.041 0.048 0.055 4 2 0 0 0.01 0.02 0.03 0.04 0.05 0.06. Extra: For an advanced challenge, you can use linear regression to further analyze your data. More to explore Draw the line-of-best-fit for your data. The spring constant is a numerical representation of the force required to stretch a material, and Hooke's law asserts that this force depends on the distance stretched or compressed. Variations: Decide how far you want to stretch or compress your spring. Direct link to levgenid's post Just above exercise 3 it . What is the spring constant k for the spring? Did all five rubber bands land close to each other or was there a lot of variation in where they fell? Ut enim ad minim. Direct link to Lucky's post In the rubber band exampl, Posted 7 years ago. Then, using the scatter plot and a line of best fit, students will determine the spring constant of the rubber band. Did they land far from where the rubber bands landed that were launched using different stretch lengths? We want our questions to be useful to the broader community, and to future users. Knowledge awaits. If you believe this to be in error, please contact us at team@stackexchange.com. Now take two rubber bands, and hold them side by side. Find the slope of the line-of-best-fit. This problem might appear different to the previous examples, but ultimately the process of calculating the spring constant, k, is exactly the same. He's written about science for several websites including eHow UK and WiseGeek, mainly covering physics and astronomy. F denotes the force, and x denotes the change in spring length. 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. F is the spring force (in N); The spring constant, k, defines the stiffness of a spring as the . The strain is the relative change in the length of the solid ($\Delta L/L_0$). Its 2*90, Posted 7 years ago. For each, $\Delta F=-k\Delta x$. Since the number of washers is equivalent to the weight, the slope reveals the weight versus displacement for the rubber band, i.e., the spring constant, which is defined as force (e.g., weight) versus displacement. In this case, the linear function fitting the straight part of the data gives a spring constant of 17.38 N/m. Use the maximum elongation as x, and the k value for each rubber band. 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. In this experiment you can check this prediction and investigate the way in which Hookes Law applies to rubber bands. 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. Why do some sources say that Rubber bands become stretchier when heated? Rubber bands stretch when we pull on them, but pulling as hard as you can on a 2-by-4 will probably have no visible effect. Create your free account or Sign in to continue. There are actually two different kinds of energy: potential energy, which is stored energy, and kinetic energy, which is energy in motion. 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. Jordan's line about intimate parties in The Great Gatsby? A fun physics problem from Science Buddies, Key concepts 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.. Shoot at least four more rubber bands in the same way, stretching them back to 10 cm on the ruler each time. No mechanical contraption would be any fun if it did not work. If necessary, have an adult do the rubber band launching. And why are the two variables directly proportional? How does temperature affect the elasticity and spring constant of a rubber band, Temperature dependence of rubber elastic modulus. The spring constant can be calculated using the following formula: k = -F/x, where k is the spring constant. If you're wondering what would your age be from a Korean perspective, use this Korean age calculator to find out. How do the graphs for Hookes law compare? Since the slope of any line on a graph has units of the vertical axis divided by the horizontal axis (slope is defined as a ratio of the change in the vertical axis divided by the change in the horizontal axis), the slope of the line-of-best fit tells you the # of washers per meter of displacement for the rubber band. Plot all points by replacing the weights with other weights and recording the new extension. What happened to Aham and its derivatives in Marathi? On stretching, they do not obey Hookes law very precisely. It may not display this or other websites correctly. 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. When an atom has more or less neutrons it is called? Suspicious referee report, are "suggested citations" from a paper mill? Elasticity of the rubber band is defined as the maximum length the rubber band stretches from its initial length when weight is placed on it. Where F F is the force, x x is the length of extension/compression and k k is a constant of proportionality known as . Be from a paper mill address ( 162.241.129.84 ) has performed an high..., and x denotes the force, and hold them side by side want our questions be. 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how to calculate spring constant of rubber band