Determining mass of a meter stick - Physics, mechanics?

Question

In the laboratory, you are asked to determine the mass of a meter stick without using a scale of any kind. In addition to the meter stick, you may use any or all of the following equipment:

1.) a set of known masses, 2.) four weight hangers, 3.) tape, 4.) a fulcrum upon which the meter stick can be mounted and pivoted, 5.) string, 6.) stopwatch

Briefly list the steps in your procedure that will lead you to the mass of the meter stick. Include definitions of any parameters that you will measure.

Indicate which pieces of equipment will be used.

Show the calculations you would perform to find the mass of the meter stick.

Answer 1

You don't need a stopwatch, or string, or the acceleration due to gravity.

Put the fulcrum one-third of the way from the left end of the stick and put weights on the left end until the stick just balances horizontally. You now have three forces at work: the weights, acting one-third of a meter to the left of the fulcrum, the weight of the left portion of the stick, acting at its center-of-gravity one-sixth of a meter to the left of the fulcrum, and the weight of the right portion of the stick, acting at its center-of-gravity one-third of a meter to the right of the fulcrum.

Let w be the weight of the stick. The portion of the stick to the left of the fulcrum weighs w/3 and the portion to the right of the fulcrum weighs 2w/3. Let your collection of weights at the left end of the stick be m.

So

m * (1/3) + (w/3) * (1/6) = (2w/3) * (1/3)
m + w/6 = 2w/3
m = 2w/3 - w/6
m = w/2
w = 2m

Answer 2

I think the instructor wants you to use balance for this experiment.

You should balance your meterstick against the set of weights. This can be done in a number of ways. It depends on what masses you use and stuff like that.

Since you have a stopwatch and you know gravity, you might want to set up the meterstick on a pully against the weights and see how long it takes either side to fall a certain distance. This gives you enough information to calculate the weight of the meterstick.

Then it just changes to one of those pully problems that they always give you.

There are a number of ways that you could solve this. Try to think of your own.