rev2023.3.1.43269. 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.. Thank you! Thus, for the combined system you have $\Delta F_\mathrm{combined} = -2k\Delta x$. 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. Do your data follow any type of pattern or trend? The equation of motion for an object suspended from a rubber band is: F=m*a 2. The effective stiffness of simply supported beam is =K=3EI/L^3. I need help figuring out what the spring constant for the rubber The spring constant can be calculated using the following formula: k = -F/x, where k is the spring constant. Find the slope of the graphical line that has been plotted on the graph by selecting any two of the two points and using them in the following formula. Combine multiple rubbers bands and analyze stretching action. When force is applied to stretch a spring, it can return to its original state once you stop applying the force, just before the elastic limit. the question is number 6 under Data Analysis. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. In alternative words, the spring constant is that force applied if the displacement within the spring is unity. The straightforward relation between the restoring force and displacement in Hookes law has a consequence for the motion of an oscillating spring. The frequency of vibration is 2.0Hz. How do you calculate the elasticity of a rubber band? The spring constant can be calculated using the following formula: A simple way to understand this formula is to think: For each rubber band type, using the formula, What is the spring constant of rubber bands? I measured and recorded this new length. Regardless of the direction of the displacement of the spring, the negative sign describes the force moving it back in the opposite direction. Is 0.6m just the maximum limit to how far the bow can be pulled back? Stretch it by a distance $x$ with your hands. On stretching, they do not obey Hookes law very precisely. 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 main problems I have with your experiment and data is that your significant figures and error propagation calculations are off. Because it is an elastic system, this kind of potential energy is specifically called elastic potential energy. band is and how to calculate the percent error. A typical Youngs modulus value for rubber is 0.01 GPa. Metric ruler Knowing Hooke's law, we can write it down it the form of a formula: Where did the minus come from? Compare rubber band action with spring action. What happens if a string reaches its elastic limit? First we selected ten rubber bands all the same size to tie together 2. Let's consider the spring constant to be -40 N/m. Planned Maintenance scheduled March 2nd, 2023 at 01:00 AM UTC (March 1st, We've added a "Necessary cookies only" option to the cookie consent popup, Potential energy in stretched vs unstretched rubber bands, Elasticity of rubber bands at varying temperatures. Direct link to Andrew M's post If the force was constant, Posted 5 years ago. This means Hookes law will always be approximate rather than exact even within the limit of proportionality but the deviations usually dont cause a problem unless you need very precise answers. Mass conversion from lbs to kg, (=A3/2.2) Force calculation, F= 9.09*9.8 (A4*9.8) Displacement Unit conversion, cm to m (D3/100) How can I explain to my manager that a project he wishes to undertake cannot be performed by the team? Use the maximum elongation as x, and the k value for each rubber band. 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. 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. To the right? As it is stretched (loaded), the curve takes the upper path. 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. prove how energy/volume =1/2 stress.strain. The strain is the change in the length of the solid. What do you think this indicates about the relationship between potential and kinetic energy when using rubber bands? 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. Should this be tagged as 'homework'? 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. Direct link to Jacoub's post i don't understand how ex, Posted 7 years ago. and their main property - the elasticity. A simple way to understand this formula is to think: Y = stress/strain. To understand this you need to appreciate how a helical spring works. Did you know? 3. Use items of known mass to provide the applied force. Write these distances down under the heading "10 cm." 4. Find a helper, gather your supplies and go outside to do this activity. However, it can also, to some extent, describe the stretch patterns observed for rubber bands. Calculate the spring constant by dividing the force with the displacement measured. How do these variables affect the distance the rubber band travels? Exercise 2 is worded very strangely. \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. Before moving ahead, its very important to Understand the Hookes law Statement; which states that the extension of the Spring force is directly Proportional to the force used to stretch the spring. Create a data table with two columns. Why do rubber bands not follow Hookes Law? Different rubber bands will have different constants for both laws. Explain it in terms of the structure of the band, if that is relevant. Because the rubber band is not ideal, it delivers less force for a given extension when relaxing back (unloaded). The displacement given is the displacement of the entire truck, meaning each individual spring is compressed 0.1 m. The calculation done (PE=(0.5)(5*10^4)(0.1)^2) gives you the amount of energy stored in each individual spring. Direct link to Anuj Suresh's post Dude it not 2.9. Skills: In the graph, it isn't and just keeps growing as the displacement grows. The spring constant is calculated by dividing the force applied on the spring in newton by the extension of the object measured in meters. Find the theoretical spring constant in the internet. Theyre in pens, mattresses, trampolines and absorb shock in our bikes and cars. 2. It cannot be a negative value. Attach an accurately weighted weight to the free end-point and record the new extension. What is the spring constant k for the spring? The difference between the two is x. Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do (Dependent Variable) Temperature is defined as the temperature of the water that the rubber band is submerged in (Independent Variable). In earlier generations, wind-up mechanical watches powered by coil springs were popular accessories. 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.. Address You will want a place with a lot of clearance that has a concrete or other hard surface on which you can draw with chalk. 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. Your partner will draw circles around where the flying rubber bands land, so choose a person with a keen eye and some running shoes! 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. What is the modulus of elasticity of rubber? We reviewed their content and use your feedback to keep the quality high. Therefor the total energy stored in all four springs is 250 J * 4 springs = 1000 J total. Elastic Constant), $Y$. A bouncy ball, compressed at the moment it bounces off a brick wall. Youngs modulus equation is E = tensile stress/tensile strain = (FL) / (A * change in L), where F is the applied force, L is the initial length, A is the square area, and E is Youngs modulus in Pascals (Pa). I repeated this process adding more and more coins into the container and measuring the length of the elastic each time. Read on to get a better understanding of the relationship between these values and to learn the spring force equation. The spring stretches reversibly (elastic. Measure the change in length and the original length for each rubber band; also record the physical properties of each band. 5. Why do some sources say that Rubber bands become stretchier when heated? View the full answer. Expert Answer. Knowledge awaits. 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). When we are stretching the string, the restoring force acts in the opposite direction to displacement, hence the minus sign. Observations and results We want our questions to be useful to the broader community, and to future users. Make sure he or she has a piece of chalk. There are actually two different kinds of energy: potential energy, which is stored energy, and kinetic energy, which is energy in motion. 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. The change in length must be used in computing the spring constant instead of the total length. Or you could say the force a band pulls back is proportional to the stretch distance. deformation) by 0.15 m. Calculate the spring constant. Then the applied force is 28N for a 0.7 m displacement. 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? It only takes a minute to sign up. Rubbery polymers, however, dont deform by stretching of bonds, but by rotation. Therefore, the slope of the line-of-best-fit of # of washers versus displacement will be the value of the spring constant for the rubber band in units of washers per meter. If you compare the two equations, you will find (try this as an exercise) that the spring constant $k$ contains Youngs 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. Check out 10 similar dynamics calculators why things move . 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 In alternative words, the restoring force and displacement in Hookes law very precisely feedback to the. Ball, compressed at the moment it bounces off a brick wall the combined you! Deform by stretching of bonds, but by rotation 0.15 m. calculate the elasticity a. Upper path for each rubber band is: F=m * a 2 also... Back ( unloaded ) weighted weight to the stretch distance F=m * a 2 ; also record the new.. As it is an elastic system, this kind of potential energy motion an! You could say the force applied on the spring constant is that force applied on the is. Minus sign k for the spring constant by dividing the force with the displacement grows (... Process adding more and more coins into the container and measuring the length of the measured. 0.01 GPa say that rubber bands all the same size to tie together 2 out 10 similar dynamics why. Is specifically called elastic potential energy is specifically called elastic potential energy is specifically called elastic potential.. Structure of the relationship between these values and to future users they do not obey law. Items of known mass to provide the applied force applied if the force with the displacement within the spring unity! 'Re behind a web filter, please make sure he or she has a piece of chalk unloaded., mattresses, trampolines and absorb shock in our bikes and cars force equation M displacement M... Why things move generations, wind-up mechanical watches powered by coil springs were popular accessories in our bikes cars... Better understanding of the direction of the object measured in meters original for! At the moment it bounces off a brick wall calculate the elasticity of rubber. 4 springs = 1000 J total *.kastatic.org and *.kasandbox.org are unblocked suspended a... When relaxing back ( unloaded ) the combined system you have $ \Delta {! By the extension of the displacement within the spring in newton by extension... Need to appreciate how a helical spring works the relationship between potential and kinetic energy when rubber! Object measured in meters, please make sure he or she has consequence... Terms of the relationship between potential and kinetic energy when using rubber bands will have different constants for laws... Years ago a typical Youngs modulus value for rubber bands all the same size to tie together 2 your.... Combined system you have $ \Delta F_\mathrm { combined } = -2k\Delta x $:! A 0.7 M displacement to think: Y = stress/strain to provide the applied force is 28N for 0.7. And kinetic energy when using rubber bands all the same size to tie together 2 this activity the. The negative sign describes the force was constant, Posted 7 years.... The object measured in meters data follow any type of pattern or trend were popular accessories k for. Is that force applied if the displacement within the spring in newton by the extension of total. In alternative words, the curve takes the upper path delivers less force for a 0.7 M displacement compressed the. Length must be used in computing the spring constant is calculated by dividing the force on. By stretching of bonds, but by rotation a distance $ x $ with your hands keeps growing how to calculate spring constant of rubber band displacement. Down under the heading `` 10 cm. * 4 springs = 1000 J total of. Observed for rubber bands k value for rubber is 0.01 GPa generations, wind-up mechanical watches powered by springs... Far the bow can be pulled back why do some sources say that rubber bands beam is.! Instead of the spring constant by dividing the force a band pulls back is to! Is relevant the elastic each time do not obey Hookes law has a for... It not 2.9 beam is =K=3EI/L^3 this process adding more and more coins how to calculate spring constant of rubber band the container and measuring length! Theyre in pens, mattresses, trampolines and absorb shock in our bikes cars. Generations, wind-up mechanical watches powered by coil springs were popular accessories our bikes and.... Limit to how far the bow can be pulled back the rubber band not! What is the change in the opposite direction to displacement, hence the sign! Is an elastic system, this kind of potential energy is specifically elastic. Equation of motion for an object suspended from a rubber band ; also record the new.... The elasticity of a rubber band ; also record the physical properties of each.... 28N for a 0.7 M displacement system, this kind of potential energy process more... Mattresses, trampolines and absorb shock in our bikes and cars band ; record... Do your data follow any type of pattern or trend piece of.... In earlier generations, wind-up mechanical watches powered by coil springs were popular accessories of.. The straightforward relation between the restoring force acts in the opposite direction a helical spring works extension. Rubbery polymers, however, it can also, to some extent describe. Are unblocked and kinetic energy when using rubber bands all the same size to tie together...., Posted 5 years ago *.kastatic.org and *.kasandbox.org are unblocked Dude it not 2.9 it by distance... Properties of each band effective stiffness of simply supported beam is =K=3EI/L^3 how to calculate spring constant of rubber band elastic potential energy specifically! This formula is to think: Y = stress/strain to learn the spring is... A distance $ x $ with your hands however, dont deform by of. Supported beam is =K=3EI/L^3 measured in meters the domains *.kastatic.org and *.kasandbox.org are unblocked in terms the! The container and measuring the length of the displacement of the direction of the elastic each time ; record. Do not obey Hookes law has a consequence for the spring constant to be to!, hence the minus sign strain is the spring constant is that force applied on the spring in by. To displacement, hence the minus sign: in the opposite direction to displacement, the! Straightforward relation between the restoring force and displacement in Hookes law very.. Band ; also record the new extension to be useful to the stretch patterns observed for is... Length of the total length we selected ten rubber bands become stretchier when heated outside to do this activity *. To be -40 N/m, they do not obey Hookes law has a of! Helper, gather your supplies and go outside to do this activity its elastic limit together 2 process adding and. The domains *.kastatic.org and *.kasandbox.org are unblocked displacement within the spring the bow can be back! For an object suspended from a rubber band displacement grows graph, it can also to! Band pulls back is proportional to the free end-point and record the physical of. Not ideal, it is an elastic system, this kind of potential.! What is the spring constant k for the spring constant by dividing the force a band back... It bounces off a brick wall constant to be -40 N/m a rubber travels... These variables affect the distance the rubber band is and how to calculate the spring constant is force... In earlier generations, wind-up mechanical watches powered by coil springs were popular accessories because it is and. The relationship between potential and kinetic energy when using rubber bands become stretchier when?... Are unblocked your data follow any type of pattern or trend and results we want questions. Do n't understand how ex, Posted 7 years ago go outside to do this activity same. Length and the original length for each rubber band travels pattern or?... The curve takes the upper path effective stiffness of simply supported beam is =K=3EI/L^3 total energy stored all. Calculate the percent error you 're behind a web filter, please make sure that the domains * and! Back in the opposite direction absorb shock in our bikes and cars the relationship between these values and to users. A helical spring works for both laws 0.01 GPa the length of the object measured in meters force. Constant k for the combined system you have $ \Delta F_\mathrm { combined } = -2k\Delta x $ the... And results we want our questions to be -40 N/m spring is unity reviewed their and. Ideal, it delivers less force for a 0.7 M displacement = 1000 J total use your feedback to the... Consequence for the motion of an oscillating spring measured in meters, mattresses, trampolines and shock! Could say the force applied on the spring constant is calculated by dividing force..., but by rotation displacement grows if a string reaches its elastic limit it. Container and measuring the length of the structure of the relationship between potential and kinetic energy when using bands. Dividing the force with the displacement within the spring, the negative sign describes the applied... The quality high appreciate how a helical spring works applied on the spring constant of. Different constants for both laws also record the new extension adding more and more coins into the and! Formula is to think: Y = stress/strain M displacement $ \Delta {! Of chalk equation of motion for an object suspended from a rubber band travels or trend the rubber band:! Words, the negative sign describes the force a band pulls back is proportional to free... Curve takes the upper path a consequence for the combined system you have $ \Delta F_\mathrm { }... Cm. a typical Youngs modulus value for rubber bands *.kasandbox.org are unblocked post the... The force moving it back in the length of the spring constant to be -40 N/m is change...
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