Measuring Gravity: Using Direct Motion Videos to Estimate g

[neilparker62]

The measurement of g appears to be somewhat limited in extent. You either have simple pendulum experiments that yield something like 10 +- 0.5 or so m/s^2 or - at the other extreme - very expensive gravimeters which will measure to a few ppb. Not much in between.

However an educationally useful site is the one with reference below which provides very useful resources by way of 'direct motion videos' one of which is of "5 Objects in Free Fall":

https://serc.carleton.edu/dmvideos/videos/five_spheres_fr.html

I have carried out some careful analysis of this video and conclude I can use it to determine g (at that location) as 9.809 +- 0.007 or so. The time data provided has resolution of 1 'frame' with the frame rate being 1500 per second. I am just wondering if somehow one could create a similar video with somewhat more accurate displacement scales - and indeed time scales so that one can use the dmv to ascertain g to (say) 5 places. I think this is about the level at which air resistance starts to affect results. For a steel ball in free fall air resistance is indeed 'negligible' - you cannot measure any discrepancy between time rising and time falling. Obviously the situation is different for the polystyrene sphere in the same dmv.

I 'enhanced' the displacement scale somewhat by using a 'pixel rule' tool on my PC but the value of g is quite sensitive to the pixel to cm conversion factor which one can only ascertain by measuring (for eg) 65 cm = 340 pixels. (ie 1.91 mm per pixel) If you alter that by just one pixel to 341, the value of g changes by about 0.008 m/s^2.

DMV equipment is not that cheap but no doubt somewhat cheaper than gravimeters (I would imagine). And the technology should enable the average school science lab to carry out experiments (such as the above) to a much higher degree of precision than was previously possible.

 

[FactChecker]

When you are looking for that much accuracy, you have recognized that aerodynamics effects each ball differently. Additionally, at anyone location, the centrifugal force from the Earth's rotation effects all of them. So before you look for more video accuracy, I think that you should insist that the test setup and the calculations be more accurate. There are also differences due to altitude and location on the Earth's surface.
Altitude of the surface can change gravity by less than 0.2% and local geology can change it by 0.01%. (see http://curious.astro.cornell.edu/ab...-across-the-surface-of-the-earth-intermediate ).

You might already know all this, but it is good to mention these other factors specifically.