|MadSci Network: Physics|
You would measure the force "given out" in the same way you would measure the force applied to stretch it, position by position with a "Newton meter" (by that I assume you mean a simple spring scale). I've never heard of anyone calculating the efficiency of a rubber band before. A heat engine, yes, a rubber band, no. I suppose it's a valid question, though. The problem with the calculation is that the force is a function of distance that you stretch the rubber band, you have to stretch it in small steps to measure this force. Then you'll have to let it contract in equal steps to measure the force of contraction at each point. If you're using a spring scale as a force meter, then you'll have to be aware that you must measure the distance the rubber band stretched and not the distance that the rubber band and scale (which will also stretch) stretched. You're not interested in the force meter, just the rubber band. Stretch the rubber band 10 cm in half cm steps or something like that, measuring the force it exerts at each point. Then, you'll know both the energy you used to stretch it and the work the rubber band did to contract. Just multiply the distance of your stretching step (half a cm is just a random number I guessed at) by the force at each point and add up all the little bits of energy to get a total. Throwing this into the standard efficiency formula for a heat engine (i.e. dividing the work out by the work in) will give an efficiency. This would be a horrible way to do the experiment, in practice, because the differences would probably be incredibly difficult to measure. Error in the measurement would be large compared to the actual measured difference. I would do the actual experiment (if this is your plan) in the following way: First take several measurements of the work it took to stretch the rubber band by the aforementioned method (measuring forces at each point, adding them up and multiplying by the incremental distance you stretched) to get a relatively accurate number for that energy. Then let the rubber band float in a calorimeter for a few hours to let everything come to thermal equilibrium (a calorimeter with as small an amount of water as possible to maximize the temperature change). Next take the rubber band out, quickly stretch it a few dozen times (wearing gloves or using two sticks to hold it in order to prevent heat transfer from your hands) and then drop it back in the calorimeter (a coffee thermos and ordinary thermometer might work, if the thermometer is accurate enough and you want to do this at home). The rise in temperature should be more quantifiable, and it will be the result of energy lost in the stretching and unstretching process. Another key to the success of this experimental method will be to make sure that when you are stretching the rubber band you make the distance you stretch it as close as possible to the full distance over which all the forces were measured. To figure out what your measurement means you will have to use some more physics. A calorimeter measures energy deposited in it by using the specific heat of water. Assuming most of the energy from the heated rubber band goes into the water, just take the rise in temperature of the water in Celcius, multiply by 4.186 (that's the number of Joules it takes to heat 1g of water 1 degree C, defined as one calorie), multiply again by the number of grams of water in your calorimeter, and divide by the number of times you stretched the rubber band. That gives you the energy that was lost heating the band per stretch in Joules. This number should be small compared to the actual energy of the stretch (a rubber band will have an efficiency close to 1), so it's good to measure it separately. Subtract this amount of energy from the total energy of a single stretch (to get the energy returned by the rubber band) and divide by that same total energy. This will give you a good approximation of the efficiency of the rubber band which eliminates most of the error associated with measuring a small change in a large number. It would be an impressive experiment if you get it to work either way. It's important to remember that the efficiency of a rubber band will probably not be a nice constant. It will be different for every rubber band you measure, and the same rubber band will have different efficiencies for different stretching distances. As it ages, of course, these numbers will change. It's kind of a messy system, despite its apparent simplicity, heat engines are much cleaner to analyze.
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