How much energy can you store in a rubber band? Obviously, the answer depends on the dimension of the rubber band.

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I'm talk about, of course, the energy thickness or particular energy the an energy storage material. The energy density is defined as the energy per unit volume, and the details energy is the power stored per unit mass. I freshly wrote around energy thickness of gasoline vs. Batteries once they're used to strength cars. But, you know, theoretically, you could power a auto with anything—including rubber bands. Just how do you determine the energy density in among those?

Let me begin with a simple rubber band that I will stretch. The cool thing about rubber bands it that they are mainly like suitable spring—but not exactly. Both springs and rubber bands have actually a one-of-a-kind property: the takes more force to stretch lock the farther girlfriend pull. Or you can say the pressure a band pulls ago is proportional to the large distance. This proportionality constant is referred to as the spring constant and is stood for by the prize k (in devices of N/m).


The energy stored in a spring depends on both the distance that that is stretched and also the spring continuous with the complying with relationship.


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So, I simply need to see if a rubber tape is "spring-like" and also then measure the spring constant. How about some real data ~ above a common rubber band—one you can find in your workdesk drawer or that one holding all your pencils together.


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You have the right to see the this mostly looks favor a linear relationship between the large distance and the force (just choose a spring). The steep of this line would certainly be the spring consistent with a value of 90.8 N/m. This means that if i stretch the rubber tape a distance of around 20 centimeters (that's roughly the break point) climate there would be 1.8 Joules of energy stored in it.


But wait! there is another means to store power in a spring. Instead of stretching it, I have the right to twist the rubber band up—you know, the method it functions on among those rubber band powered balsa lumber airplanes. The pretty thing around winding a rubber band up instead of stretching is that it doesn't really take up much more room together you store power in it. Also, it releases energy while unwinding in a much more controlled fashion 보다 it would certainly by stretching.

However, if the feather doesn't stretch then it's pretty hard to measure the feather constant—so i will simply do miscellaneous else. If i measure the torque required to twist the rubber tape I have the right to do miscellaneous very comparable to the linearly stretched rubber band. In this case, I have the right to measure the twisting torque v a force probe put a fixed distance indigenous the axis the rotation. Right here is my plot of speak vs. Rotation angle.


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This looks prefer a relatively linear relationship—just choose the extending vs. Force. The slope of this line mirrors the relationship between twisting angle and also torque—I will contact this the rotational spring constant (kr). Because that this rubber band, I have actually a rotational spring constant of 3.68 x 10-5 Newton*meters. Now I can calculate the complete energy v this expression (you can derive this for homework).


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So, how much energy can I keep in the rubber band this way? I can twist the rubber band with 100 changes without breaking it (it damaged at 111 rotations). This would certainly be a complete energy warehouse of 7.2 Joules. That's odd. It appears I have the right to store an ext energy by twisting quite than stretching.

Before calculating the power density, I first need the rubber tape volume. If you take it a rubber band and cut it, it simply becomes a yes, really long and thin cuboid. Every I must do is measure up the length, width and height. Because that this details rubber band, I obtain a volume of 8.1 x 10-7 m3. This would give a rubber band energy density of 2.2 MegaJoules/m3 for stretching and 8.9 MegaJoules/m3 because that twisting. That can seem favor a most energy, however remember the 33gasoline has actually 34 GigaJoules/m3.

Oh, what about the details energy? Again, this is just the energy stored per unit mass. The rubber band has a fixed of 1.09 grams. This puts the specific energy at 1651 J/kg because that stretching and also 6605 J/kg for twisting. Is that useful? If girlfriend are building a rubber tape powered car, yes—that will certainly be an extremely useful.

What happens if you use a gigantic rubber band? I discovered this super size rubber tape in the office (no idea what its purpose is). Let me quickly repeat the energy density calculation just for comparison. Right here is a plot of the twisting torque vs. Rotation angle.


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The rotational spring continuous for this thicker tape is not surprisingly higher than the normal sized rubber band, through a value of 4.92 x 10-4 N*m. If ns assume that ns could also rotate this one 100 times, it would have an energy storage that 97.1 Joules. Of course it stores more energy, but it also has a better volume. After measuring the dimensions and also calculating the volume, I get an energy density of 6.4 MJ/m3. That's right about the same energy density as a little rubber band. Ns think that's pretty cool. Perhaps I need to repeat this measure for every sorts that rubber bands. Or probably I can just leaving that up to you because that a homework assignment.


Rhett Allain is an combine professor the physics in ~ Southeastern Louisiana University. He enjoys teaching and talking about physics. Occasionally he takes things apart and also can't put them ago together.

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