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Hypothetical brain teaser here, no real kittens involved! -

For some bizarre reason I have a sack of kittens, I need to find the total weight of the kittens and the sack but I'm only allowed to use a spring scale and I'm only allowed use my arms to hold the scale. My arms are unsteady and the kittens are constantly moving around in the sack, causing the weight display on the scale to dance around wildly.The kittens all weigh different weights and they are in constant motion. I am wondering if it is possible to very accurately get a reading from the scale, perhaps by incorporating some kind of accelerometer? This has been puzzling me for some time!

Looking forward to hearing your input.

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Use Kalman filter, augmented by a model of kitten movement. –  Deer Hunter Aug 16 '13 at 8:44
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My answer to the weighing your head question also applies here: send the kittens to space. Eventually they will suffocate and stop squirming. Then you a constellation of microsatellites to measure the mass. –  Michael Brown Aug 16 '13 at 9:10
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The part about the kittens jumping is easily solved, If you measure sufficient data, and average correctly. How to average data the data is another issue that one has to work out correctly. if you attach the accelerometer to you hand you can subtract the effect of the movement of your hand easily. –  Prathyush Aug 16 '13 at 10:53
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This is akin to weighing a gas no? Assume the pressure applied to the bottom of the sack to average over a large enough time scale. I think it's fair to assume the wriggling is gaussian and so a time average is a fair measure to compute... –  Nic Aug 16 '13 at 11:30
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Why can't you just average many measurements. –  ja72 Aug 16 '13 at 14:47
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1 Answer 1

If we assume the air-resistance is negligible you can just average all the measurements - the jumping kittens will average themselves down to epsilon sooner or later.

If you also start and stop the measurements when your arm is in the same position and you make sure there are no swinging of the bag involved the error induced by your arm moving will be evened out because of energy conservation.

If the bag is swinging around it will induce centripetal forces to the spring scale (making the bag look heavier than it really is). The kittens will have a hard time inducing this if the bag can rotate freely from the scale.

Your arm is then the only thing being able to induce swinging motion. If you could find a way to estimate the bag+kittens center of mass you could measure the amount of centripetal forces and remove these from the scale-measurement. Kalman filters is cool for this.

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