Uniform Circular Motion

[emzz]

Hi,

We did the uniform circular motion experiment in school a few days ago in which we tied a rubber stopper to a string and swung it in a horizontal circle overhead. In our practical report we are required to list down some of the random and systematic errors that could have occured during the course of the experiment. Can someone help please?

Also, how do you determine the mass of the stopper from the graph of F (nett force) vs T^2 (sec^2)?

Thanks.

[InfiniteNow]

If I recall, F = ma. So, you determine acceleration (using distance and time), and put that number in for "a," and you put your force number in for "F" and solve for m. I think...

Wind could have given random perturbation to the swinging string.
Strangeness in muscle contraction. A hiccup, a sneeze... An overall increase in the elasticity of the rubber band. There could have been a tremor in the earth like a mircro earthquake. The heating/cooling system in the building may have turned on and blown air toward the stopper. Oh, and there's always quantum randomness.


Maybe someone can check the appropriateness of my F=ma comment, but the ideas should get you moving in the right direction in terms of systematic errors. Gook luck on the assignment.

[emzz]

Thanks a lot!
My teacher said he won't except human error as an answer though so that rules out hiccups and sneezing! Lol. And no heating/cooling system or fans were turned on during the course of the experiment.
But i think i get the idea

[Pyrotex]

Originally Posted by emzz

...experiment in school a few days ago in which we tied a rubber stopper to a string and swung it in a horizontal circle overhead. In our practical report we are required to list down some of the random and systematic errors that could have occured during the course of the experiment. Can someone help please? Also, how do you determine the mass of the stopper from the graph of F (net force) vs T^2 (sec^2)?...

Whatcha got here is your basic equilibrium of forces. There's the outward centripetal force on the stopper, and there's the inward (radial) force holding the string. The way we did it in freshman physics was have the string go through a loop, go downward, and tie off at a known mass. The stopper is spun enough so the known mass is suspended.

Inward force, Fi = ma. this is known mass times 'g', the accelleration of gravity.

Outward force, Fo = Mrw^2, where r is string radius, M is mass of stopper and w is angular speed in radians per second. If the stopper goes around once per second then w = 2*pi radians/second.

Since the spinning stopper is holding up the known mass there is equilibrium, and Fi = Fo.

Your worse sources of error are (in order):
friction, friction and friction.

[emzz]

Thanks, pyrotex
By friction you mean air resistance? Could you explain in a little more detail please?

[InfiniteNow]

Oh, friction could apply to all manner of things.

In the most basic sense, it's loss of energy due to molecular collision. There is friction in the rubber band, in it's connection with the stopper, and, yes, air resistance as well. Pyrotex is much better versed in these matters than I, so hopefully he will respond as well, but you might check out the following in the meantime:

Force

Or, if that's too high level, check out the following then come back to the previous.

Resistive Force of Friction - Succeed in Physical Science

[Qfwfq]

A note of caution:

Originally Posted by emzz

My teacher said he won't except human error as an answer though so that rules out hiccups and sneezing! Lol.

He probably meant mistakes in measurement. If the setup was what you describe I'd count in the fact that it is a highly irregular dynamic system, full of unknown parameters. Actually that would be the major source, even without hiccups or sneezes.

[emzz]

Rite. Thanks for all your help !
Just one more question, the stopper is suppose to swing horizontally. However, when we did the experiment, we swung it at a slight angle at times. Would this affect the results at all? If yes, why?

[Pyrotex]

Originally Posted by emzz

Rite. Thanks for all your help !
Just one more question, the stopper is suppose to swing horizontally. However, when we did the experiment, we swung it at a slight angle at times. Would this affect the results at all? If yes, why?

InfiniteNow and Q [yes, the same one from Star Trek tng ] answered your questions as good as I could have done.

The answer to this question is "yes" -- it will affect the results. But not by much. If the angle, phi, between the horizontal plane and the plane of your stopper's circular motion is small, say, less than 5 degrees, then the error introduced will be approx equal to sin(phi)*Mg which would be less than 0.014 times the mass of the stopper times the accelleration of gravity.

This error would increase (add to) the centripetal force where the orbit of the stopper "dipped down" and decrease (subtract from) the centripetal force where the orbit of the stopper "tipped up". This would be felt as a slight oscillation in the outward force. If your inward force is being measured by a spring scale, then you would see the error as a slight flutter of the scale pointer.