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I'm sure you all have held a common retractable, spring-loaded pen at least once, and that many of you have tried to make it jump vertically by first pushing it downward against a table to load the spring (and then a second time to release it). But have you ever wondered what happens to it after the first click, when it returns to its mechanical equilibrium, while still touching the table*? Will it be longer, shorter, or the same length?

*this last condition is crucial, for else there might be different answers depending on the type of pen. Alternatively, you can assume it has no "loose" parts, or that there is no gravity.

EDIT: As Penguino has pointed out, there is still more than one answer depending on the type of pen. But do try it with the pens you have at home! (Though there is only one interesting case)

P.S. I hope this is not too trivial for this forum, but I thought this might be a nice little puzzle to bring up with friends.

The Footprint
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    I never did, my interest was dropping an unretracted pen from a height above the desk to see what the minimum height is to release the catch and rebound higher than where I dropped it from, and of course, I have to catch the pen. I must explore this new pastime. – Weather Vane Jul 07 '20 at 19:54
  • Oh, I did this in my childhood, we even used to have an adventure-pen-game: the story of a pen who jumps the highest, lol. Anyway, sorry I don't quite understand, what is the difference between the premise (the first sentence) and the question? – athin Jul 07 '20 at 23:30
  • @athin sorry I don't follow you. I'm basically asking if the pen will change in length after you click it. – The Footprint Jul 07 '20 at 23:51
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    @athin - this is how I interpret the question. (1) place a pen, pen retracted, button-end down, on a table. (2) click the pen down (3) while keeping the pen in contact with the table release it back into mechanical equilibrium. pen should be extended now (4) is the pen taller/shorter than it was in step 1? – user46002 Jul 08 '20 at 00:06
  • @Hugh what is retracted/extended in your comment, the thruster or the nib? If you mean the latter, you are right, otherwise just switch the two states. – The Footprint Jul 08 '20 at 01:55

1 Answers1

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I think it will still be either shorter or longer depending on the type of pen.

In an old-style BIC pen, the 'push-rod' that clicks the pen is in rigid contact with the end of the cartridge/nib. So when pushing down on the body of the (upside-down) pen, the nib will be pushed out at the business end and the catch will hold in the little side slot. But unless the tip of the nib was already exactly level with the end of the pen body, the pen will now be shorter by the length of the 'underlap' - distance X below.

In many newer pens - the ones that you can re-click by pushing down on the end, rather than by applying sideways pressure on the catch, - there is initially a gap between the push thingy and the end of the cartridge. In these pens, the nib is pushed out and an internal catch holds it in place, after which the push thingy (in equilibrium) is pushed back out by a second spring so (at equilibrium) it is protruding the same amount as it started at. In this case, the pen is now longer by the distance Y below.enter image description here

Note: both of my pens have very blunt nibs and the catch mechanism itself isn't drawn exactly realistically. But I don't think that changes my argument.

Penguino
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  • I didn't know the second type you describe existed, the ones I tried were either old-style or had a loose thruster. I thought there couldn't be a second spring because it wouldn't accomplish anything beside making the pen harder to click. But thank you, I will correct my question. – The Footprint Jul 08 '20 at 10:27
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    And, as soon as I posted, I noticed a third variety sitting on the edge of my desk where you click-turn the body to make the nib protrude. But those ones don't jump so probably not relevant to this question. – Penguino Jul 08 '20 at 21:08
  • I guess that would still be either in the first or second group? As far as the answer to my problem goes. I wager that it would be in the first group, because if the thruster turns and clicks it probably doesn't rebound after pushing the cartridge. – The Footprint Jul 08 '20 at 22:43
  • Yep - gets longer but doesn't rebound at all. – Penguino Jul 09 '20 at 00:07