|MadSci Network: Physics|
Dear Anne, While I think doing experiments to test scientific theories is a wonderful thing, it is always very important to make sure they are safe experiments. Trampolines, unfortunately, can be very dangerous, especially if they are not surrounded with a safety net. Many people end up in the emergency room with broken bones, or worse, for trampoline injuries. How about doing this as a Gedanken experiment, which was one of Einstein’s ways of experimenting? A Gedanken experiment is a “thought” experiment, that is, one that you do in your head. You can think of a trampoline as a platform on a spring on which you are standing. Please take a look at this website where I have drawn a diagram for you (http://www.gpc.edu/~jguinn/MadSci/Trampoline.pdf). The strength of the spring (trampoline) can be described by the spring constant, “k”. The larger “k” is, the less the spring, or trampoline, will compress or stretch for a given weight. A very tight trampoline (large “k” value) would stretch down only a little if you stood on it, a very loose trampoline (small “k” value) would stretch a lot. The more weight you put on the trampoline, the more it will stretch. We can measure the amount of stretch by the displacement, “x”, which is the distance the spring goes down. These three quantities are roughly related by the equation Weight equals Spring constant times Displacement , or W = k x . So what would happen if you put weights on a person on the trampoline? Well, you would be increasing their total weight, and so, to start, the trampoline would stretch more, a little more if “k” is big, a lot more if “k” is small. How high would they go? Now that depends on how hard the person starts jumping. When someone first climbs on a trampoline, the trampoline stretches and the person stands without moving on the somewhat stretched trampoline. To get them flying in the air, the person needs to start pushing with their legs to get the trampoline to stretch more. As the person starts squatting down and pushing up, they are pushing more on the trampoline, and increasing the displacement. This makes the trampoline push back on them more, that is, with more force. If the person keeps doing this, the force from the trampoline can get so large that it tosses them right into the air. How will their weight affect this? The heavier the person is (it doesn’t matter if it’s their own weight or added weights) the harder they would need to push to get them moving. It’s just like jumping into the air; it would be harder for you to jump off the ground if you’re wearing a heavy backpack, than if you aren’t. The trampoline would have to push a heavier person harder to get them to the same height as a lighter person, and the heavier person would have to do more work to get the trampoline to stretch enough to do it. The end result of all this is that a person with extra weights wouldn’t necessarily go higher than when they didn’t have the weights. As a matter of fact, they would have to worker harder to go as high as they could without the weights! Well, Anne, I hope I’ve answered your question. Again, let me emphasize, please be careful on your trampoline, I certainly wouldn’t want you to get hurt! Good luck and have fun thinking of more physics experiments! Please let us know if you have any more questions. Sincerely, Jim Guinn Georgia Perimeter College
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