How to measure the released energy?

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Hi, guys! I am a high school senior, I would like to ask you a few questions about how to measure the released energy during physics experiments, especially both nuclear reactions.

Also, how could Fermi just know the "yield" just by a handful of torn paper?

As the shock wave hit Base Camp, Aeby saw Enrico Fermi with a handful of torn paper. "He was dribbling it in the air. When the shock wave came it moved the confetti. He thought for a moment."

Fermi had just estimated the yield of the first nuclear explosion. It was in the ball park.[13]


Fermi's strips-of-paper estimate was ten kilotons of TNT; the actual yield was about 19 kilotons

Thanks for your reading!
 
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Well unfortunately there isn't an exact "paper movement" to "yield of an atomic bomb" formula. I'm actually doing a research paper about this right now, so I've sifted a lot of information. The test date there was relatively no wind. My best guess on how he actually calculated this was by some formula on the force of the shock-wave, if he knew how far he was from the blast, and the loss the force would encounter of a distance. With how far the paper traveled he could then determine the shock-wave force at his location. He could then use these numbers to determine the yield. I'm no physics expert but that's how I'd have to say. Fermi was an interesting guy, he claims he invented the first nuclear pile (reactor) while walking down the street. Observers said he didn't stop for any cross-walk lights that day. To put it simply though, he was 50% off, which really isn't that bad for being a nuclear bomb and I've reached 300% error in labs. He's a pretty interesting guy to read about, I'd recommend the books: The making of the atomic bomb - Rhodes. It's quite funny, an observer says Fermi was making bets if the bomb would ignite the atmosphere, and whethere it would destroy New Mexico or the world. I can't imagine being there and having him question these things I'd just be thinking "what did i get myself into?" Well I know I got a little off topic but I hope I answered your question and sparked some interest. The nuclear bomb development is an amazing topic, endless amounts of information.
 
I actually just found a quote from the book "The making of the atomic bomb" - Rhodes


Fermi had prepared an order-of-magnitude experiment to determine roughly the bomb's yield:"

"About 40 seconds after the explosion the air blast reached me. I tried to estimate its strength by dropping from about six feet small pieces of paper before, during and after the passage of the blast wave. Since, at the time, there was no wind, I could observe very distinctly and actually measure the displacement of the pieces of paper that were in the process of falling while the blast was passing. The shift was about 2.5 meters, which, at the time, I estimated to correspond to the blast that would be produced by ten thousand tons of T.N.T."

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