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Yes objects do weigh more whilst moving in elevators. This is due to energy mass equivalence that Einstein detailed through the well-known e=mc2 equation. An object in an elevator is moving and therefore has kinetic energy, which translates into more mass. This increase, however, is extremely minute and not measureable with normal scales (even down to .000001 of a pound) because the mass increase is the amount of energy divided by 8.98755179 × 1016 (the speed of light squared).

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