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Explain how the weight of an object can change while its mass remains constant.

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The weight of an object is dependent on the environment while mass remains the same in all environments. This is because weight is the gravitational force applied on an object. Mass is the property of the object. Check out http://en.wikipedia.org/wiki/Mass for more information.

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It could be on a different planet. Weight is the force gravity has on it pulling it towards the center of earth. Every planet has a different value.

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Weight is related specifically to the gravity applied to it. So long as the gravity around the object changes, its weight will change (while its mass is not).

Such answers include: taking it far away from the earth, putting it on the moon, etc.

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your mass will be constant because the mass is the matter your made up out of while the weight is not part of the matter your made up out of