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from falling through the floor,
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but also accelerate you counter to what gravity wants to do.
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That's why it is g plus a.
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So, you picked up some speed,
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then you're coasting along at a steady speed.
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Then, a drops out and you weigh your normal self.
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As you come to the top of the building,
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the elevator has to decelerate,
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so that it loses its positive velocity and comes to rest.
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So a will be negative
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and w, in fact, will be less than mg.
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So, you will feel weightless for a short time