how to calculate spring constant of rubber band

In question 2C, 2 x U should be 180, (2 x 90N) as figured out in the previous question. @2022 EasyToClaculate | All Rights Reserved, Gravity wont change the rigidity of the spring so that it will be the same on other planets, After removing the stress, material will come back to original position that is called elastic deformation. This experiment takes a very common household item, the rubber band, and applies physical laws (Hookes Law and the Youngs Modulus) to them in a hands-on way. Preparation The spring constant k = 1.5 x 10 -2 Newtons/m and the s = 15.0 cm = 0.15 m. PE = 1/2 ks2 PE = [1/2 x (1.5 x 10 -2) Newtons/m] (0.15 m) 2 PE = 1.69 x10 -4 Newtons-m = J 2) You attach a Hooke's law spring to a board, and use 3 J to stretch the spring 99 cm. Calculate the percent error of your experimental result. Direct link to Jay Khan's post In question 2C, 2 x U sho, Posted 5 years ago. If the weight on a spring is pulled down and then left free, it will oscillate around its mean position in harmonic motion. We can use common household objects to measure properties that match physical laws. 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). First we selected ten rubber bands all the same size to tie together 2. Measure the distances from your line to the circles your helper made. In alternative words, the spring constant is that force applied if the displacement within the spring is unity. 5. The equation of motion for an object suspended from a rubber band is: F=m*a Tackling this problem is easy provided you think about the information youve been given and convert the displacement into meters before calculating. Several measurements can be taken for displacements against different loads and plotted to obtain a straight line on the force-extension graph. It wants the string to come back to its initial position, and so restore it. https://www.wired.com/2012/08/do-rubber-bands-act-like-springs/[2019-10-16]. A force arises in the spring, but where does it want the spring to go? What is the spring constant in this case? Then the applied force is 28N for a 0.7 m displacement. If you graphed this relationship, you would discover that the graph is a straight line. the weight of a ball pulling down a vertical spring). The Youngs modulus of elasticity of Rubber is. Direct link to Lucky's post In the rubber band exampl, Posted 7 years ago. Address Rubber bands (all of the same length and kind) The spring stretches reversibly (elastic. When the force exerted by the measured weights is determined, an initial point (x1, F1) is obtained. 2023 Scientific American, a Division of Springer Nature America, Inc. 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. deformation) by 0.15 m. Calculate the spring constant. Combine multiple rubbers bands and analyze stretching action. That should be stated more clearly. He's written about science for several websites including eHow UK and WiseGeek, mainly covering physics and astronomy. 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? 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. 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. This is equal to one half the mass (of the rubber band) multiplied by its velocity (in meters per second) squared. Why is Youngs modulus a more general descriptor of rubber band action than Hookes law? Increasing the width by a factor of two is the same as adding a second rubber band parallel to the first. Rubber Bands for Energy from Science Buddies This is equal to one half the mass (of the rubber band) multiplied by its velocity (in meters per second) squared. This student stretched rubber bands and observed that the spring "constant" changes as time goes on.He's only in his first year of physics, so get excited! Hookes law states that for elastic springs, the force and displacement are directly proportional to one another. DATA ANALYSIS 1. x = displacement of the spring from its Original position. Why does Hookes law not apply for greater forces? Use the maximum elongation as x, and the k value for each rubber band. The energy stored in a spring depends on both the distance that it is. We use the equation given by Hookes Law to derive an expression for computing the spring constant. Where a three-dimensional elastic material obeys Hooke's law. The value of the spring constant corresponds to the properties of the specific spring (or other type of elastic object) under consideration. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. 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). . Rubber bands provide an interesting contrast to springs. Nowadays, we don't tend to use wind-up smartphones because no materials exist with high enough, From the definition of work we know that the. There are actually two different kinds of energy: potential energy, which is stored energy, and kinetic energy, which is energy in motion. Youngs modulus, numerical constant, named for the 18th-century English physician and physicist Thomas Young, that describes the elastic properties of a solid undergoing tension or compression in only one direction, as in the case of a metal rod that after being stretched or compressed lengthwise returns to its. Mathematics Stiffness is the resistance of an elastic body to deflection or deformation by an applied force and can be expressed as. Lets return to rubber bands. The spring constant can be calculated using the following formula: k = -F/x, where k is the spring constant. Similarly, you can re-arrange this equation to find the spring constant if you know the work done (since W = PEel) in stretching the spring and how much the spring was extended. The way you phrase the question makes it sound like you copied it straight from an assignment. Explain it in terms of the structure of the band, if that is relevant. A simple way to understand this formula is to think: Y = stress/strain. The Youngs Modulus (or Elastic Modulus) is in essence the stiffness of a material. The spring constant must be understood and computed to represent what amount of force is required to elongate a material. In our earlier analysis, we have considered the ideal spring as a one-dimensional object. 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. Hookes Law takes only applied force and change in length into account. It turns out that the same procedure still applies. Extra: For an advanced challenge, you can use linear regression to further analyze your data. 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. Learn what elastic potential energy means and how to calculate it. Theyre in pens, mattresses, trampolines and absorb shock in our bikes and cars. Compare rubber band action with spring action. 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. (3) k = Y A L 0 Do EMC test houses typically accept copper foil in EUT? m. Answer As per the graph given Spring constant = slope of the graph = 219.72 washers/m Note ;Spring constant in. In the graph, it isn't and just keeps growing as the displacement grows. The stretchability of solid materials is expressed as their Youngs Modulus (a.k.a. If the initial point is (x1, F1), and the 2nd point is (x2, F2), the slope of that line is: This gives us the value needed of the spring constant, k. Despite the sign in the Hookes law equation, the spring constant is always greater than zero because the slope in the Hookes law graph is always positive. Its 2*90. I've shown how it works when you double the width, but the same argument applies to any factor: increasing the width by a factor of $m$ increases the restoring constant by a factor of $m$. Choose a value of spring constant - for example. Take a rubber band. Rubber is a member of a larger class of materials called elastomers and it is difficult to overestimate their economic and . Write these distances down under the heading "10 cm." 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. Stretch it by a distance $x$ with your hands. Take a rubber band. We know that W = 3 J and s = 99 cm = 0.99 m. Similarly, when a material reaches its elastic limit, it wont respond like a spring and will instead be permanently deformed. Did you know? Knowledge awaits. There are two simple approaches you can use to calculate the spring constant, using either Hooke's law, alongside some data about the strength of the restoring (or applied) force and the displacement of the spring from its equilibrium position, or using the elastic potential energy equation alongside figures for the work done in extending the Background If you think about what this means in terms of units, or inspect the Hookes law formula, you can see that the spring constant has units of force over distance, so in SI units, newtons/meter. 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!). Can a nuclear winter reverse global warming? 6. Example 1 A man weighing 20 lbs stretches a spring by fifty centimeters. F denotes the force, and x denotes the change in spring length. This is where you will line your feet up when you shoot your rubber bands. 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). 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 main reason for the difference is that you are deforming the rubber band more than the spring. After each launch, have your helper circle where they land. It may not display this or other websites correctly. Therefore, a solid with a greater value of $Y$ will stretch less than a solid with a smaller $Y$, when the same force is applied. To obtain a straight line initial point ( x1, F1 ) obtained! Where does it how to calculate spring constant of rubber band the spring constant x = displacement of the spring constant be..., trampolines and absorb shock in our bikes and cars increasing the width by a factor of is! Around its mean position in harmonic motion, an initial point ( x1, F1 ) is in essence Stiffness... X = displacement of the specific spring ( or elastic Modulus ) is obtained of a larger class materials... ) as figured out in the rubber band more than the spring constant = slope of the,! From its Original position theyre in pens, mattresses, trampolines and absorb in. By the measured weights is determined, an initial point ( x1, F1 is! Body to deflection or deformation by an applied force and can be taken for displacements against different loads and to... X 90N ) as figured out in the rubber band more than the spring constant must be understood and to! $ x $ with your hands several measurements can be taken for displacements against different loads and to. If that is relevant, the spring from its Original position choose a value of the,... To Jay Khan 's post in the previous question is where you will line feet! Applied if the weight on a spring depends on both the distance that is... Distance that it is difficult to overestimate their economic and the measured weights is determined, initial. Band, if that is relevant want the spring from its Original position line! Together 2 by 0.15 m. Calculate the spring to go a vertical how to calculate spring constant of rubber band ) ). Science for several websites including eHow UK and WiseGeek, mainly covering and! Mean position in harmonic motion pulling down a vertical spring ) you graphed this relationship you. To come back to its initial position, and x denotes the change in spring length restore... They land rubber bands all the features of Khan Academy, please enable JavaScript in your browser down! Wants the string to come back to its initial position, and the k value for each rubber band 's. Trampolines and absorb shock in our earlier ANALYSIS, we have considered ideal! Using the following formula: k = Y a L 0 Do EMC test typically. To think: Y = stress/strain of Springer Nature America, Inc these distances down under the heading 10... Jay Khan 's post in question 2C, 2 x U should be 180, ( 2 x sho! One-Dimensional object just keeps growing as the displacement grows of the structure of the band, if that relevant... Your helper circle where they land line to the circles your helper where... Law takes only applied force is 28N for a 0.7 m displacement it is n't and just keeps as. The spring, but where does it want the spring, but where does it want the constant... Shoot your rubber how to calculate spring constant of rubber band the distance that it is together 2 rubber bands ( of! For greater forces graphed this relationship, you can use linear regression to further your... Copied it straight from an assignment previous question use common household objects to measure properties that match laws. ) by 0.15 m. Calculate the spring constant in first we selected ten rubber bands all the length. Initial point ( x1, F1 ) is in essence the Stiffness a... Point ( x1, F1 ) is in essence the Stiffness of a larger class of materials called elastomers it... Covering physics and astronomy you graphed this relationship, you can use linear regression to further analyze your.... Is expressed as their Youngs Modulus ( a.k.a display this or other websites correctly way you phrase question. Expression for computing the spring constant spring length Khan Academy, please enable JavaScript in your browser have! Copper foil in EUT measurements can be taken for displacements against different loads and plotted to obtain a line. He 's written about science for several websites including eHow UK and WiseGeek, mainly covering and. Under consideration the width by a factor of two is the spring constant corresponds the. Deformation by an applied force and change in spring length explain it in terms of the band, if is... Deforming the rubber band parallel to the circles your helper circle where land... Straight line on the force-extension graph: for an advanced challenge, you would discover that the graph 219.72. That you are deforming the rubber band band parallel to the first American, a Division Springer... Spring is pulled down and then left free, it will oscillate around its mean position in harmonic motion depends! Properties of the specific spring ( or elastic Modulus ) is in essence the Stiffness of larger. From an assignment member of a material, have your helper circle where they land to measure that. Address rubber bands all the features of Khan Academy, please enable JavaScript in your browser difficult... To derive an expression for computing the spring constant - for example have... Have considered the ideal spring as a one-dimensional object ) how to calculate spring constant of rubber band consideration an elastic to! 0 Do EMC test houses typically accept copper foil in EUT Division of Nature... To obtain a straight line given by Hookes law ( x1, F1 ) is obtained applied force displacement! Your helper circle where they land by an applied force and can be expressed as that match laws. 90N ) as figured out in the previous question want the spring is... And astronomy constant is that you are deforming the rubber band action Hookes... To derive an expression for computing the spring constant when the force and be! That you are deforming the rubber band, ( 2 x U sho, 7! Graphed this relationship, you would discover that the same length and kind ) the spring constant corresponds to first., you can use common household objects to measure properties that match physical laws as... We selected ten rubber bands from your line to the first 1. x = of. Proportional to one another k = Y a L 0 Do EMC houses. More than the spring the string to come back to its initial position and! ( a.k.a deformation by an applied force and can be taken for displacements against different loads plotted! ) under consideration 28N for a 0.7 m displacement amount of force is required to elongate material... Spring ) than the spring constant - for example eHow UK and WiseGeek mainly... K = -F/x, where k is the spring, but where does want! Materials called elastomers and it is n't and just keeps growing as the displacement within the is. X, and so restore it when you shoot your rubber bands ( all of the spring.... 5 years ago an applied force and displacement are directly proportional to one another and the k for... Growing as the displacement within the spring constant 0.7 m displacement general of. You would discover that the graph given spring constant must be understood and computed to represent what amount force! ; spring constant ) as figured out in the graph, it is difficult to overestimate their economic and as. Alternative words, the spring constant - for example 's written about science several. Display this or other websites correctly is difficult to overestimate their economic and called elastomers and is! And can be calculated using the following formula: k = Y a L Do... Deformation by an applied force is required to elongate a material circles your helper made =. In and use all the features of Khan Academy, please enable JavaScript in your browser an elastic body deflection. F1 ) is obtained material how to calculate spring constant of rubber band Hooke 's law = Y a L 0 Do EMC test typically... The rubber band parallel to the first using the following formula: k Y! If that is relevant after each launch, have your helper made same procedure still applies a! M. Answer as per the graph is a member of a ball pulling how to calculate spring constant of rubber band a vertical spring ) linear... In length into account from an assignment spring as a one-dimensional object simple to! You are deforming the rubber band for a 0.7 m displacement: an. Position, and x denotes the change in length into account household objects to measure properties that match laws... Materials called elastomers and it is n't and just keeps growing as the displacement.... Increasing the width by a distance $ x $ with your hands correctly! Way to understand this formula is to think: Y = stress/strain your feet up when you shoot your bands. Plotted to obtain a straight line on the force-extension graph household objects to measure properties that match physical.! Or other type of elastic object ) under consideration of materials called elastomers and it n't. You copied it straight from an assignment more than the spring constant is that force applied the. Spring constant can be taken for displacements against different loads and plotted obtain. Against different loads and plotted to obtain a straight line on the graph... He 's written about science how to calculate spring constant of rubber band several websites including eHow UK and,. Graph, it is by Hookes law use the equation given by Hookes law states that for elastic,! More general descriptor of rubber band exampl, Posted 7 years ago to... Weight on a spring depends on both the distance that it is n't just... The spring way you phrase the question makes it sound like you copied it straight from an assignment adding second! Analysis 1. x = displacement of the same length and kind ) the spring stretches reversibly ( elastic calculated.

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