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The person's body does not change density, but when you put a life jacket, you and the jacket can be modeled as one object. The life jacket itself has a very low density, much lower than that of a human. So, when you put on a life jacket, you effectively increase your volume, while mass increases by a much smaller degree. As a result, net density decreases.

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Q: Why can humans change their density using a life jacket?
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