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Does a closed cage with an helium balloon weigh the same as an empty closed cage? What if the balloon isn't touching the ceiling ? (It's a tall cage and we're weighing it in the process of the balloon elevating)

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It makes no difference whether or not the balloon touches the ceiling. The weight of the cage can always be determined from the contained mass, which is less with a helium ballon inside.

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  • $\begingroup$ why is it less? $\endgroup$
    – Shmoopy
    Jan 9, 2014 at 18:55
  • $\begingroup$ Because the cage is not fully filled with heavy air but some of it is filled with light helium. Think of a solid metal bar as opposed to a metal bar with an air bubble inside. $\endgroup$ Jan 9, 2014 at 19:03
  • $\begingroup$ Because the helium has a lower density than the air it displaces. If the balloon floats, the helium is sufficiently lighter than air to cover the weight of the balloon. $\endgroup$ Jan 9, 2014 at 19:03
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    $\begingroup$ I should add, that it does make a difference, if the balloon if accelerating upwards as this moves the balance point down (it moves heavy air downwards). This is like dropping a heavy ball inside the cage. As long as the ball is stationary or moving with constant velocity its weight will simply add to the weight of the cage. When the ball is in free fall it will not. So when the balloon is accelerating upwards the weight of the cage will appear lower. $\endgroup$ Mar 25, 2014 at 10:22
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A closed cage with a helium balloon doesn't weight the same as an empty cage because the mas of a helium balloon adds to the the mass of the empty cage. A cage with a helium balloon doesn't weight less it floats (according to the Archimedes Law) in a more dense medium.

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