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That is the force which I do not know in magnitude.
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But this is the acceleration of the one kilogram mass.
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Then, I bring the elephant
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and I pull the spring by the same amount
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and I find the acceleration of the elephant
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and the denominator is obviously the mass of the elephant.
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The force is not known,
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but it's the same force.
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So, when I divide these two numbers,
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I'm going to find a1 over aE is equal to mE over m,
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which is the one kilogram mass.
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What we needed was some mechanism of exerting some fixed force.