The mass of a match

Homework Statement

Find the mass of a single match. You are only allowed to use the following things: a ruler which weighs 10 gramms, and a matchbox full of matches.

The Attempt at a Solution

Well I havent tried anything yet since its kind of hard to get this thing rolling.
But since its an olympiade question, not a homework one, I guess its no hurry.

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Do you have any suggestions/ideas?

Not really, I wouldnt know where to even begin.

I suggest a possible starting point would be to count how many matches are in the box...
(Can you guess why?)

Because we need the mass of a single match. But I dont think its much of a starting point.

I dont know exactly how many are there, but I dont think it makes much difference at this point. We also got to count in the mass of the box. We could probably find it with removing the matches from the box and testing it separatedly.
But test how? I dont know. Thats the question.

Another way I can think of would be to measure the size of the match, calculate its volume and multiply by the density of wood. But we would also need the density of the tip, which is carbon? Or phosphorus, sulfur? Thats where it would get a tad inaccurate. But I dont think thats the way it has to be done.

Thats pretty much all I can think of at the moment.

Last edited:
ehild
Homework Helper
Balance the ruler on your finger with the box full of matches at one end, then repeat it with the empty box. You know the mass and length of the ruler. You can read the position of the box from the axis of rotation (your finger), so you can calculate the torques at both sides...

ehild

Balance the ruler on your finger with the box full of matches at one end, then repeat it with the empty box. You know the mass and length of the ruler. You can read the position of the box from the axis of rotation (your finger), so you can calculate the torques at both sides...

ehild
God damnit. Why didnt I think of that?

Thanks ehild !

God damnit. Why didnt I think of that?
Sadly, the reason you didn't think of it, was because someone told you the answer before you had had time to reason it out for yourself. (A much better educational outcome)
I was under the impression that these pages were not the place where someone else answers the question for you, but where they provided you with a clue or some help to enable you to work it out for yourself.
(This is not a criticism of fawk3s)

ehild
Homework Helper
God damnit. Why didnt I think of that?
:
Because you did not try to play with a ruler and a box of matches. Your idea was not bed either, to measure the size of one match or more of them with the ruler, and estimate the mass from the volume and density.

I suggest you to try. Which method is more accurate? Maybe you find some other way to solve the problem.

ehild

The question "Why didnt I think of that?" was actually meant to show my emotion on how easy it actually was. But the thing is, I dont think I would have thought of that myself. It did seem a kind of a hint that they gave you the mass of the ruler though.

I dont think it was a bad thing either that the answer was given out so fast, because there was another, quite similar problem which I kept wondering a year back and which I had forgotten all about. I couldnt figure that out by myself. But now its as clear as day to me.
So I guess it did educate me a little.

Thanks again you guys!