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What do I need? What would the most effective method be to reduce the uncertainty of my outcome? Should I record the mass and diameter of the marble too or just the height? If I change mass will it be more effective than height change?

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  • $\begingroup$ Exactly what do you mean by the "size" of the crater? Is it how deep it is? How wide it is? $\endgroup$ – Bob D Nov 3 '20 at 17:32
  • $\begingroup$ If I recall correctly, NASA has done experiments on crater size vs. high velocity impact speed. $\endgroup$ – David White Nov 3 '20 at 18:22
  • $\begingroup$ I don't know what constraints your experiment has or what kinds of conditions it will be done under, but I recommend you compare your results to my favorite approximation in physics! Check out this answer and this answer for details on the approximation. Check out the other answers on the first post in particular, where a much more detailed analysis gave similar answers. $\endgroup$ – tpg2114 Nov 3 '20 at 18:52
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How do I investigate the affect of height of the fall of a marble on the size of a crater in sand?

It really depends on what you mean by the "size" of the crater. Are you talking about how deep it is? How wide it is?. Also, toy marbles come in a variety of sizes and are made of a variety of materials.

If you want to maximize the depth of the crater, then for a given mass and height of the fall you would want the marble with the smallest diameter, i.e., the marble of the greatest density. This will maximize the impact force per unit area of sand.

On the other hand, if you want to maximize the width of the crater, then for a given mass and height of the fall you would want a marble with a larger diameter in order to maximize the diameter of the crater.

Regarding mass vs height, the kinetic energy of the marble upon impact with the sand will be $mgh$. The greater the kinetic energy the greater the size of the impact, all other things being equal. So if you double the mass you can halve the height to get essentially the same size impact, and vice-versa.

You can approximate the depth of the impact by equating the kinetic energy upon impact with the work done by the sand to bring the marble to a stop. Or

$$mgh=F_{ave}d$$

Where $F_{ave}$ is the average impact force and $d$ is the depth of the crater, ignoring the loss of gravitational potential energy over the distance $d$. The combination of $F_{ave}$ and $d$ will depend on the "hardness" of the sand. The harder the sand, the less the depth of the impact and the greater the average impact force, and vice-versa the softer the sand.

Hope this helps.

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