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Can we convert the EPE of a stretched rubber band (x=10 cm) to the Work that is done as the rubber band is launched? (Work = Force x distance traveled through the air)? Or do these two things not correlate? I thought the EPE should be similar to Work done (not while being stretched, but while flying through the air). But when we converted cm to m, we got vastly different values (recorded in Joules). Help!
Question Date: 2020-01-22
Answer 1:

Initially, when the rubber band is stretched, all of its energy is stored as elastic potential energy (EPE). The amount of EPE is proportional to the square of the distance you stretch the rubber band (in fact, it is equal to (1/2) x (the square of the stretch distance) x (an elastic constant that depends on the material). When you release it, that energy transforms to kinetic energy (KE). KE is equal to (1/2) x (mass of the rubber band) x (the square of the velocity).

If you could measure the velocity of the rubber band right after release, you would find that there is a linear relationship between the stretch distance and velocity. Unfortunately, it is hard to measure velocity directly- but as you mention, it is easy to measure the total distance travelled by the rubber band! More on this in a minute.

First, back to your question about work. Once the rubber band is released, it isn't doing any work: although it travels a distance, it is not applying a force. If you did this experiment in space, you would expect the rubber band to keep going forever! The reason it stops here on earth is because eventually, gravity makes it fall, and once it hits the ground, all of its energy is quickly lost to friction.

But the distance travelled is still a useful quantity that we can relate to the EPE. The travel time of the rubber band is just how long it takes to fall vertically (plus a little bit of time sliding on the ground- this will depend on the friction on the surface). Now, assuming the rubber band is shot perfectly horizontally, the time it takes to hit the ground won't depend on its EPE at all- only on gravity and the height at which it starts. So if you start the rubber band at the same height every time, it will hit the ground after the same amount of time- but, a faster band will be able to travel further during that time. So the distance the band travels will be (approximately) proportional to its initial velocity... which (as discussed above) is proportional to the amount the band is stretched! Thus, if you test several different stretching distances, and measure the travel distance for each one, you should find a linear relationship between them. If you are interested in doing this experiment yourself, Scientific American has a guide with more detailed explanations of the physics:


A note: if two quantities (such as "distance stretched" and "distance travelled") are proportional, it means there is a linear relationship between them: if you double "distance stretched," you would expect "distance travelled" to double as well.

Answer 2:

I am not exactly sure what EPE stands for in this context; I am going to assume it means elastic potential energy.

However, work is not force X distance traveled through the air. Work is equal to the combined kinetic and thermal energy gain of the rubber band when fired, of which the kinetic energy will be equal to one half times the mass of the rubber band times the square of its velocity. The distance traveled will relate to its velocity, and if it is fired horizontally in a vacuum it would be proportional to the kinetic energy, but you're firing it in air, which means that it will be slowed down due to drag. The rubber band would also go farther if fired partially upward instead of horizontally, as well, even with the same amount of kinetic energy.

It is also possible that you made a math error in unit conversions, or in working with the algebra. Joules are a unit of energy that includes meters, not centimeters. It would be probably easier if you converted the spring constant to meters in the first place.

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