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If I write on the starting page of a notebook, it will write well. But when there are few or no pages below the page where I am writing, the pen will not write well. Why does this happen?

Fattie
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Ram Keswani
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    The physics here are quite different between a ballpoint pen (which I assume is the subject of this question) and fountain pens (which write based on capillary action and require very little if any pressure); between those, a rollerball uses liquid ink that requires less pressure to transfer, so you might not observe this so acutely when using one. – Charles Duffy Oct 08 '17 at 17:11
  • To check the ideas in the answers, try a good fountain pen that works with zero force. – JDługosz Oct 14 '17 at 02:59

2 Answers2

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I'd say the culprit is the contact area between the two surfaces relative to the deformation.

When there are other pieces of paper below it, all the paper is able to deform when you push down; because the paper is fairly soft and deformable fiber. If there is more soft deformable paper below it, the layers are able to bend and stretch more.

(A simplified example of this is Springs in series, where the overall stiffness decreases when you stack up multiple deformable bodies in a row)

This deformation creates the little indents on the page (and on pages below it; you can often see on the next page the indents for the words you wrote on the page above). The deeper these indents are, the more of the ballpoint is able to make contact with the surface.

Ballpoint pen tip up close

If there is barely any deformation, then the flat surface doesn't get to make good contact with the page. This makes it hard for the tip of the pen to actually roll, which is what moves the ink from the cartridge to the tip. It would also make a thinner line due to less contact area.

Here is an amazing exaggerated illustration I made on Microsoft Paint:

Pens on page in paint

The top one has more pages, the bottom one has fewer. I've exaggerated how much the pages deform obviously; but the idea is that having more pages below with make that indent larger; leading to the increased surface area on the pen tip.

Note that this doesn't really apply to other types of pens. Pens that use other ways to get the ink out have less of an issue writing with solid surfaces behind; but ballpoint pens are usually less expensive and more common.

JMac
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    Very nice answer. I write with fountain pen most of the time, and with those the issue doesn't arise - as you point out in the last paragraph. – Floris Oct 08 '17 at 14:27
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    I work at a retail store that prints receipts on thermal paper, which is very slick. Most of our budget ballpoints won't write at all on a single piece over the hard desk. – Asher Oct 08 '17 at 17:02
  • Not saying your paint skills are bad in comparison, but, the photo looks a lot cooler than the paint drawing. Did you do that yourself or by google-fuing? It is such a cool image, and I had never seen the ball of the pen that close (and dirty). – Vendetta Oct 11 '17 at 15:56
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    @Vendetta https://en.wikipedia.org/wiki/Ballpoint_pen#History I don't think I have the photography equipment or skills to take a picture like that. – JMac Oct 11 '17 at 16:28
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    Hey, at least you have the google-fu skill to complement your lack of photographic prowess. – Vendetta Oct 11 '17 at 16:35
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    shouldn't friction be added to the answer as well? on hard surfaces friction will be less and sliding will be more? – Sarthak Mittal Oct 12 '17 at 08:26
  • I'm not sure if I buy this. Say we were talking about: sheets on inch thick, and a ball, say, 10 inches diameter. In that theoretical example, sure, "pushing down" would give more contact area of the ball on the top sheet - so in the 10:1 example, sure, the effect described in the answer here is real. However I don't think that is ratio domain for actual paper and pen-balls. The ball is so small that the "squash" of just one sheet of paper (and indeed, one sheet of paper is quite squashy) is huge compared to the ball. – Fattie Oct 14 '17 at 13:15
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    @Fattie Common printer paper is 0.1 mm thick; ballpoints are commonly 0.7 mm. The ball is 7x larger than the paper. If the paper could compress until it had no thickness (not happening), it could compress through ~3.5 sheets before it reached the ballpoint housing. Because of the decreased stiffness in series, having more paper below it also makes it easier to "squash" the paper. If you have one piece on a hard surface, you would need to push harder (and even then; you can only make a 0.1 mm indent at best; and that's by pushing through the page). – JMac Oct 14 '17 at 17:16
  • hey @JMac - that' – Fattie Oct 15 '17 at 12:23
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On a base/bed of several soft paper sheets the steel ball of the pen makes a better deeper contact by indentation with side cushioning. The contact area diminishes when just a few pages of a notebook are left with less padded cushioning. In metals also a Brinnel hardness tester leaves a deeper permanent impression on softer metal than on hardened material.

Somewhat like the difference between out of control forced skiing dragged down after a fall in thick snow and the normal glide skiing.

Narasimham
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