|MadSci Network: Earth Sciences|
It sounds like you've got an interesting project there. In your question, however, there are a lot of hints that you have done a variety of experiments and are asking for a specific answer about only one thing. Maybe that isn't the real thing you need to look at......
You mention sand "with the smallest grains" which implies you are trying different target materials, and you imply that the smallest grain size of sand doesn't show the increase in crater size you expect.
My "experience" is all second-hand and with hypervelocity experiments but I'm sure a lot of the concepts will carry across, so let's look at the situation....
In meteor craters, either on the Earth, the Moon or any other body, the volume of the crater scales approximately with the energy of the impact. The radius (or diameter) should scale as the cube root of the energy. In your case gravitational potential energy accumulates with height so you might expect an increase as the cube root of height. Thus the crater diameter will initially increase rapidly, then drop off as the height goes up. This might look like a drop off in crater growth vs drop height, especially if you don't measure very carefully.
If this isn't happening, you can investigate a number of other possibilities...
1) Has the marble reached terminal velocity?
Well, what IS the terminal velocity of a marble? I think it's more than you'll get by dropping it from 2.5m. You can test this, even if you can't measure the speed, by dropping one a long way (many stories of a building, for example) and examining the effects. Be careful to protect yourself and others from stray falling marbles and from glass splinters though!
Or you could throw a marble into the box and see if you can make a larger crater, even if you don't know the exact speed. At least you'll know that you can get larger craters. You could also build a catapult to fire the marbles at controlled high speed, and callibrate it.
2) Is it something to do with the grain size?
Different materials behave differently in an impact, especially at the slow speeds you're looking at. Try flour, sugar, salt, sand, plastic beads, rice grains etc. You'll find that shape, size, density all matter. Perhaps your fine sand is somehow packing into a stiffer more resistant form on impact? Try a different type of sand (sharp, builders, aeolian, sandpit ....). It may be that your fine sand has different shape or size distribution than the coarse ones. Sand isn't just sand, you know.....
3) Is it something to do with the layer depth?
You don't say how big your craters are, but a marble is 1 cm and the crater must be bigger than this. If the size of your crater is comparable to the depth of the layer (which it will be) then special effects operate. The trouble is, the impact energy will be transmitted into the target as a "shock" wave (I use inverted commas because a true shock wave has special properties. Yours might only be a sharp energy pulse). This wave will travel outwards from the impact site, tending to open up a crater radially but will also have a large downwards component. When it hits the solid base of the tray it will at least partially reflect back upwards. It may be that the arrival of this reflected wave back at the surface actually does much of the job of forming the crater. If you try a deeper sand layer you may get different results, or try different trays. wood vs steel, expanded polystyrene or maybe a rubber liner? How about doing the work outdoors in a big sand pit?
(In hypervelocity impacts like meteors, the impact energy is turned into a vast explosion with much less directionality, but the momentum of the impacting body still has to be properly accounted for.)
4) Is it something to do with the imact energy, or the impacting body?
If you extend your measurements over a much larger range of energies, you may see that your observed anomaly is a temporary effect over a limited range of energies as the morphology of the crater changes from one type to another.
How about getting the same energy from a smaller faster (or denser) body. Shoot a small ball-bearing in, or an air gun pellet. What influence does the size and or shape of the impacting body have?
There's a lot you can find out here. Good luck.
If you want to discuss this further, email me here on the other side of the world - firstname.lastname@example.org
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