Friday, March 04, 2016

Physics Brain Teaser: Bee in a Jar

Imagine you've got a jar on a scale, sealed so that no air can escape. Inside this jar, there's a bee hovering in place. Does the scale read more, less, or the same as when the bee is resting at the bottom of the jar?

Image Credit: Elder Scrolls Wiki
At first blush, you might think that a hovering insect's weight shouldn't show up on the scale, but you'd be mistaken! If the jar is sealed and the bee stays at a constant height, it doesn't matter whether the material propping it up is air or glass—it's exerting the same amount of force on the scale. If you've ever been around a helicopter while it was taking off or landing, you might have felt a fraction of the rotors' power as air was forced downward and then, having nowhere else to go, outward. The total force exerted on the ground by the helicopter must be equal to the helicopter's weight in order to keep it aloft at a constant height, but since the force is transferred through air, it's spread out. Since our bug is in a jar, however, and the jar is sealed, there's no way for the air (and the downward push imparted onto that air by the bee's wings) to disperse. As a result, the air molecules colliding with the bottom of the jar have more force than those colliding with the jar's other surfaces, and it acts heavier—as though the bee were sitting still on one of the jar's interior surfaces.

What would happen if the bee were to flap faster or slower, and rise or sink in altitude within the jar? Post your answers in the comments below!

7 comments:

  1. faster/slower: shouldnt matter as long as the bee is still floating in place, rising at constant speed = weight of bee+jar weight, accelerating up = larger than constant speed, accelerating down = less than

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    1. If you imagine that the bee is just made of air (having the same weight/mass as the amount of air displaced by its presence in the jar, then it is obvious that whether the bee flaps its wings, sits on the bottom of the jar or clings to the sides or top, will make absolutely no difference. Regardless of what the bee does, or where in the jar the bee is located, is irrelevant. The jar will always weight the same.

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  2. if the bee flaps faster in order to rise up with an acceleration (with increasing speed in upward direction)...the scale will read more than when bee is hovering at fixed height(h) with constant speed in that cross-sectional plane which is height(h) above the bottom.

    If the bee is falling freely from some hight towards the bottom then scale will only read weight of jar.....not the bee.

    If the bee is falling freely and suddenly manages to stop at some height then change in momentum of bee will also be reflected in display of thee scale(weighing machine) along with weight of jar.

    there are many more ways the bee can move to changing the display of scale....it depends up to what decimal place the scale could show the reading...as there are many factors which can account for change of display of scale....for example even the humming and buzzing of can can show considerable change in overall weight if scale is accurate enough to show differences up to 7 decimal points.

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  3. I would expect a falling bee to result in a lower weight scale reading.

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  4. flapping faster or a lower altitude, I would intuit, would increase the weight due to increased friction.

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  5. If the bug stays at a constant height, its weight is shown on the scale. if it moves upward, it will have to move wings faster and more force will be exerted on the air molecules and thus reading on the scale will be more. if it moves downwards, then reading on the scale will be less.

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