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Name: Vinay
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How can the sum of potential energy and kinetic energy be constant when a helium balloon moves up in air as both potential energy and kinetic energy increases?

The potential energy is going _down_ as the balloon rises. This is counter-intuitive because the standard way of describing potential energy is based on the assumption that gravity is much greater than the buoyancy (buoyancy is ignored). But that is not a good assumption with the helium balloon. Potential energy is actually stored in the submerged (in air) helium balloon -- to help visualize, think of how much work it takes to submerge a basketball under water. With the basketball, you are pushing water up (it is displaced by the ball) against gravity, storing potential energy. It works the same way with the balloon submerged in air. Filling the balloon displaces air, thereby storing potential energy in the balloon. When you release the balloon, that potential energy is converted to kinetic energy (there are other factors as well -- it expands as it rises, for example, but I will neglect those for purposes of this answer).

Hope this helps,

Burr Zimmerman

The potential energy of the helium balloon increases as it ascends, but as it ascends it allows heavier air to descend to take its place. The air's potential energy thus decreases. The decrease in the air's potential energy is of greater magnitude than the increase in the helium balloon's potential energy, so overall potential energy decreases.

Richard E. Barrans Jr., Ph.D., M.Ed.
Department of Physics and Astronomy

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