How Can I Accurately Measure Gravity Using a Pendulum in My Lab?

[ccflyer]

"Little G" Lab Suggestions

Hey everyone,

My goal is to find the Acceleration due to gravity to five significant figures. I think that I will use a pendulum to do the lab with, but am looking for suggestions for what I should use to measure distances and/or time with.

For measuring time, my school's stopwatches only have 3 significant figures. I was thinking that I might try to use a computer timer of some type, but havn't found any software yet (havn't really had the time to look for that yet).

Any suggestions on technique or tools would be greatly appreciated.
Thanks,
Chris

 

[HallsofIvy]

Same thing Gallileo did- use an inclined plane to slow down the accleration to a measurable quantity.

 

[FredGarvin]

You're never going to get 5 sig figs out of anything requiring human interaction, like a stopwatch. Your reactions alone will introduce more error into the experiment than anything. You need to "slow down" the entire process which is what Halls was mentioning with an inclined plane.

 

[LENIN]

I would say it's almoust imposibel. The best resoults I maneged to get in my school lab where 2 digits. It's really hard to get better ones becouse of friction air resistance and stuff like that. If you use good equipment you might be abel to get 3 digits but I doubt that you could get more.

 

[LeonhardEuler]

It would be relatively easy to set up a circuit with an IR emitter and detector that can be triggered by the pendulum. The 555 is a cheap (less than a dollar) timer chip that is easily available (at radio shack, for instance, but you'll pay too much), and it gets quite a bit of precision. The difficulty will be in divising a circuit that will count the 555's pulses. While this is not too dificult in an absolute sense, it may be going too far over the level of the course. And 5 sig figs is a lot. You'll run into trouble getting the 555 pulse to be exactly what you want it to be because you need resistors and capacitors to set it, which have at best 5% error. The way to solve that is to let the clock run for a very long time and see how many pulses go by with a watch. The time you wait should be so long that the time it takes you to click your watch is negligible. You then use the pulse length you measure, rather than trying to tweak it to what you originally wanted which would take forever. The best solution to these problems is to get a crystal oscilator with a pre-determined cycle length, but these are harder to come by.

 

[LeonhardEuler]

There are also ways of measuring "g" that don't require measurements of time. For example, measuring the stretch in a spring when it holds up a wieght. In that case, kx=mg, so you need a spring for which the value of k is known to high precision, a way of measuring distances to high precision, and a wieght whose mass is known to high precision. This might be very difficult to do, but maybe someone else can expand on this idea to make it easier.

 

[LeonhardEuler]

Oh, and how could I have forgotten the classic Atwood machine? It is just two blocks of different masses attached to opposite ends of a string which is placed over a pulley. If you work out the free body diagram for the situation you will see that the expression for the acceleration involves the difference of the masses, which means the acceleration can be made quite small by making the masses almost the same. Just google "Atwood's machine" for more info.

 

[andrevdh]

Chris,
doing high precision experiments require skills and equipment that only professionals have access to. If you just need the value it is best to get it from someone else like the Geology departement of a university. The problem with the inclined angle suggestions above will be that you still need to measure the inclination of the plane to a high degree of accuracy. The gravitational acceleration varies with lattitude and elevation. Sears, Zemansky and Young gives the following values in their fifth edition of University Physics:

 

[ccflyer]

Hey thanks everyone for replying.

I really do need to do the actual experiment for a lab grade, so just obtaining the value that someone else measured won't really work, but will help me find percent error (thanks andrevdh for those values). I think that I'll try to stay away from the spring idea because of the shortage of precision springs at my school. I guess that I'll try to go with the inclined plane method although I do know it will be VERY hard to get the timing right and the angle exact enough.

-Chris

 

[andrevdh]

Check out: http://www.sfu.ca/phys/233/labscripts/expt01.pdf It gives instructions to determine g using an air track.

 

[Kazza_765]

I think the only way you are going to do this is to think big. If you can measure accurately to 1mm, you need a 10m pendulum to get 5 significant figures. A 10kg weight will do if you can measure to 1g (but you should be able to do better than this in a high school lab), oops, you don't even need to measure the weight. Measuring time will be the hard part.
So you buy the highest strength fishing wire you can find (I don't know much about fishing but 15kg is only a few dollars so surely you can manage something much stronger) hang it out a third story window and attach a really large weight. Hopefully if you can use a large enough weight air resistance and internal friction will be negligable. Then set it swinging and measure how long it takes for 20 cycles. This should be in the order of 120 seconds, so if you stopwatch goes to .01s you have 5 significant figures. Realistically your going to have to do this many times to eliminate the human error factor, and your still likely to have margins of error in the order of .1s but I can't think of any other way to get your required accuracy.