So I was given this physics project to do as a final ISU project. Engineers onl

[simms]

Well, I'm in a senior level physics class, and our final ISU is to find the mass of an unknown object. That easy. We can employ any factors known to physics, including but not limited to Hooke's law, deflection of objects, compression/expansion, ballastic pendulums and such. The thing is, there's a number of ways mass can be solved using physics, but we need the most accurate one available.

Our mark depends on how accurate our value is compared to the real one based on a digital scale. We CANNOT read the value off the system we create, nor can we purchase a system - we have to fabricate it from our own materials. I realize error is based upon systematic and random error, but WHICH system is most accurate?

Our physics teacher has stated a few examples:
- Hooke's Law (using period vs mass, or extension vs mass) - Basically a slinky on a piece of plywood with the deflection of the object measured.
- Compound system - two spring attached to one central balance - Haven't done this one, don't know how it works.
- Cantilever system - measuring the deflection when the object placed at the end of a ruler, persay with the other end flat on a table.
- Initeral (sp?) system - same as cantilever, but you measure the deflection sideways (so it swings back and forth)
- Ballastic pendulum - A period with 10 oscillations with the mass on it, period is given and mass is solved using a pendulum.
- Compression - Not sure, basically mass is put on a spring and deflection is measured how much the spring 'sank' down.
- Something about Young's modulus might work too, but I have no idea how that works.

I forgot to state that the unknown mass is within a given range of 100g-2000g.

So there are 5 methods. Which would you recommend is the most precise, or if you know of another system, please mention it.
-Simon

 

[jonnylane]

ok

this is really interesting because you have to find the answer to a seemingly simple problem.

First off, i'd say that any ballistic techniques would be a bad move, since you're messing with drag, extensibility of your "rigid" string and all sorts of madness. It can be accounted for approximately but its not the best way to do it.

Hookes law/spring? Well, its a good idea because its not a dynamic system. The problem lies in measurement. Say you have a spring attached rigidly to a place off the floor. The mass is attached the other end. You now have to measure the extension of the spring, which is off course due to the force applied (mg). You will need to be as accurate as possible with parallax errors. I'd recommend using a camera (digital would be best) fixed on a tripod, in front of a good scale. you can then measure the extension accuratley.

But,ah,you say, how do i know what extension refers to what force applied?

well, you will need to calibrate the system by adding known weight to the spring and measuring the extension of the spring. You can then get a calibration graph with which to read off your extension of the unknown weight.

i won't go into any more detail, since you are supposed to be doing it, not me.

What do you think?

 

[simms]

Your response was what I needed to know. I had already thought of using Hooke's law as my first method of doing so, and I already know how to calibrate, etc etc. :) What I need to account for is the mass of the SPRING ITSELF - say I use a SHM (Simple Harmonic Motion) with Hooke's Law, eg: The spring is held by a retort stand on a table, with the spring dangling below.

The camera seems like a good idea and is feasible, but wouldn't the measure of how high I adjust my tripod still have parallax? If I use a camera I still can't expect to get it dead on.

By Hooke's Law, do you mean COMPRESSION of the spring or EXPANSION of the spring? I only did expansion because I figured compression would be too hard to find extension for.

-Simon

 

[jonnylane]

you've made several good points.

I don't think [?] you need to know the mass of the spring, because when you hang the spring, it extends itself under its own mass. If you then take the bottom of the point, parallax permitting, as zero extension that takes care of that.

Parallax wise, its a little more tricky than i thought. here's a few (slightly silly) ideas:

1) weigh the camera (a light one) and attach that to the mass,take the photos, and then subract it off at the end.
2) I've actually used this one (!). Get an area uniform light source (like one of those things they use to look at x rays)and place it behind the system. attach a ruler to a white screen, and measure the position of the projected shadow.

i have a few other ideas, but they require some thought...

 

[simms]

This was posted on another forum that I asked the question on and I was wondering if you knew anything about it:

"If the teacher will only allow one spring to be used then you could use a moveable pivot so that you can adjust the moment (ratio) of the balance arm. If you put a stop so the spring can never be over extended (keep from skewing results from deformed spring) and adjust the pivot with the weight in its dangling basket until the spring is extended to a set distance. This will increase your accuracy. You would just throw the ratio of the pivot arm in with the distance and K to get your weight. "

Picture here: http://pics.bbzzdd.com/users/WarCon/Experiment.jpg

-Simon

 

[jonnylane]

pic doesn't work, but i get the idea.


i think this person is saying that when the spring is extended, just move the supporting rod so that the end of the spring doesn't move. I don't see the point personally.

his reason for using this method is that the spring will deform as it starts to reach its elastic limit, ie, out of the linear region. The way to counteract this is just to use a good spring that has reasonable extensibility for the weight you are using, without it being too weak, ie, never reaching its elastic limit.

you can work out how far the spring will stretch given a weight added to it if you know hookes number, stress/strain. springs usually have this information included in packaging. alternatively, you can just do it by trial and error.

 

[simms]

To make the picture work, COPY the text link, and paste it into the URL window of a new IE box. Or you can click and drag the link onto another address bar and it will load. If it doesn't work, I'll host it elsewhere.

 

[jonnylane]

well, its theoretically a more accurate system i suppose, but in terms of a school laboratory setup i don't think you'd be any better off error wise.

if you do a quick experiment (with known weights) on the spring you will be using, it will be easy to predict, via a graph, where the elastic limit will be approximately. as long as you stay well away from this force, you won't have a problem.

just remember the error in the extension is goverened by the size of the extension. Its a compromise between acceptable error and ruining the spring.