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Q & A: An ant dropped off the Empire State Building

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Q:
If you dropped an ant of the empire state building, would it die due to the impact, or would air dispacement bring it to the ground safely?
- Sean (age 28)
Bedford
A:
The force of gravity on an ant is really tiny. If there were no air, an ant (and everything else) would accelerate at 9.81 meters per second per second. The resistive force due to air drag increases with the speed and opposes the motion. Eventually, an object goes fast enough so the drag force is equal and opposite to the gravitational force, and the object no longer accelerates. We say it has reached "terminal velocity".

The terminal velocity for an ant in air is quite small -- no more than two meters per second, I guess (having dropped a number of ants from about a meter myself). Ants are also amazingly durable -- they have very hard exoskeletons. I think the ant will have no trouble surviving that fall!

Some ants even have wings and can fly!

Tom

(republished on 07/30/06)

Follow-Up #1: Changing Terminal Velocity (of an Ant)

Q:
What if I place the ant on something much heavier, like my school bag for example? Then there would be no air resistance, so would it die?
- Z (age 14)
Singapore
A:
If the ant clings to something much heavier, like a school bag, then there will in fact be much more air resistance. In addition, the force from gravity will be much larger, and able to overcome this air resistance. Thus, the terminal velocity will be much greater.

You can predict this effect qualitatively simply because the force of gravity scales with volume (since this is proportional to the total mass), while the force of air resistance scales with surface area. So, if you double the object's dimensions, the force of gravity goes up as length cubed, and the force of wind resistance goes up as length squared.

These effects are important: heavy sky divers fall appreciably faster than light ones, and so use larger canopies.

So yes, the ant will probably be squashed, unless your school bag has a parachute inside.

David

(published on 05/18/13)

Follow-up on this answer.