Re: [Phys-l] projectile motion lab

[Hugh Haskell <hhaskell@mindspring.com>]

At 12:16  -0400 10/9/06, fizix29@aol.com wrote:
> I used a student's sample of about 50 time measurements, that is, 
> the time it took the marble to roll between the two photogates.  I 
> used the mean time and the distance between the two photogates to 
> calculate the speed of the marble as it rolled off.  I used the 
> standard deviation of the time measurements as the error in the time 
> and a reading error of +/- .5 mm for the distance measurement.  When 
> I carried the calculations through (I also measured the height of 
> the table to +/- .5 mm) I found that the range of the projectile was 
> only certain to about 30%.  It could be as low as 20 or as high as 
> 40 cm.  That hardly seems a triumph for newtonian mechanics!  There 
> must be a flaw in my assumptions.  I confess I am only now beginning 
> to include rigorous treatments of error and uncertainty in my labs. 
> It was a fault of my youth I am trying to correct!
Since you don't mention the SD of your initial velocity measurements, 
I can't tell exactly why your distance measurements have so large a 
spread, but it seems to me that the problem lies in the initial speed 
off the edge of the table. And that could be driven by any number of 
factors--imprecision in the release point of the ball at the top of 
the track; the way the bottom of the track merges with the table top 
(a sudden change in direction will lead to bouncing of the ball which 
could have fairly large effects on the speed of the ball at table's 
edge--a smooth curved transition from incline to horizontal will help 
that). If the timing is done with a photogate and they are placed 
close together, small errors in timing can have relatively large 
effects on the calculated speeds. If the timing is done by hand, 
there will be a relatively large SD in the time with a similar 
variation in the calculated speed which could account for the large 
variation in the distance.

Photogates will likely have a rather larger gap between the sending 
and receiving sides that the size of the object passing through them, 
and so the actual time of starting or stopping the timer can be 
affected by the position of the ball as it passes through any gate, 
closer to one side or the other. If one looks at the actual signal 
that passes between the arms of a photogate as an object passes 
through, it will be seen that the signal does not go suddenly to zero 
but decreases at a more moderate pace. The choice of the point in the 
signal roll-off where the time actually shuts off, is the source of 
most of the imprecision in photogate timing, and the actual shape of 
this curve is surprisingly sensitive to the shape and position 
relative to the arms of the object passing through.

It has been my experience that the main lesson learned in experiments 
like these is the extreme sensitivity of the results to the initial 
conditions. This seems also to be true of measurements of g. It also 
turns out that the initial conditions are rather hard to control with 
sufficient precision, and, they are frequently neglected as a source 
of imprecision.

Hugh
--

************************************************************
Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

When you are arguing with a stupid person, it is a good idea to make sure that
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					Anonymous