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Energy (エネルギー, Enerugī) is sometimes used vaguely to mean "a force that affects an object", such as heat, electricity, or gravity, but strictly speaking, it is a kind of accumulation of these forces.
It can be calculated by integrating force over distance or work rate (power) over time.
Work is used in the same sense, but it is used in the sense of "difference in energy" (like the difference between position and distance).
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Quantity Joule Calorie Solar Potential Heat Electricity Gravity
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エネルギーとは [単語記事] - ニコニコ大百科 (NicoNico Encyclopedia)