Does a Hammer Fall Faster Than a Feather?

Cecil's Columns/Staff Reports
1

I was browsing the archives and noticed a certain “babynous” asking whether his physics professor had been correct in saying that (in a vacuum) a feather and hammer fall at the same rate. Babynous thought that “the total force between Earth + hammer” would be greater, due to the difference in the mass of the hammer, and so that (in accordance with the “ignorant layman’s” intuition), a hammer actually would in fact hit the ground first.

The Staff Member Ian gave the expected condescending answer, in which he lectured that the extra force on the hammer is exactly cancelled by the extra mass of the hammer, so that its acceleration equals that of the feather.

However, I think this misses babynous’ point. What he was saying is that the Earth also gets pulled UP by the feather and the hammer, and that the hammer pulls it up faster than the feather does.

To restate babynous’ idea in a clearer manner: If we conducted two separate experiments, one in which a feather was dropped from a height of 1 km onto the Moon, and one in which a ball the mass of the Moon was “dropped” from one kilometer above the Moon, surely it would take longer for the Moon and feather to make contact. This is true even though the acceleration (relative to a fixed third point) of the feather would be the same as that of the massive object.

Bob Murphy
NYU

2

I have made this point exactly. However, on a practical note, the 'force" of the hammer would be insuff to overcome the intertia of the earth, of bring it out of orbit. However, when they bring out that calculation to show that there forces exactly equal out, ask them this- in the classic “two-body” problem, is the mass of the “other” object of no inport at all?

But is this not better for GQ?

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First off, Bob, welcome to the Message Boards, and congrats on your first post.

Second, please, it would help if you would cite the link to the column or Mailbag Answer that you are referencing, so everyone can be on the same page (so to speak): If a feather and a hammer are dropped together, won’t the hammer hit the ground first?

And, finally, please note that there was extensive discussion, comment, hypotheticals, and what-not on this topic already:
http://boards.straightdope.com/sdmb/showthread.php?threadid=2685
and
Galileo, a hammer, and a feather

… and, I think, a few other places.