(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello! I am an honors physics student and i have been assigned a project that has puzzled me. I have a container full of sand, a couple meter sticks, a tennis ball, and a stopwatch. What I need to do is prove something through the use of these items. What I am going to try to do is prove that an object dropped from a taller height will create a bigger impact crater. This is a very elementary concept, I know. I just don't know how to mathematically relate the crater depth to the increase in energy. I see that with the height increase, the total energy increases. But how do I directly relate the crater depth to the energy increase? I can find the velocity before the impact, how do I factor in the velocity of the impact?

2. Relevant equations

Ke=1/2MV^{2}

Ep=MGH

Vf^{2}=Vi^{2}+2AΔX

3. The attempt at a solution

I am planning on conducting 25 drops: 5 from .5 meters, 5 from 1 meter, 5 from 1.5 meters, 5 from 2 meters, and 5 from 2.5 meters. With each height increase, I am expecting an increase in crater depth. I am just confused on how I am going to prove mathematically that the height increases crater size. I know that the combined energy before the impact will increase because Kenetic energy=1/2Mass * velocity^{2}(Ke=1/2MV^{2}) and potential energy=Mass * Gravity * Height (Ep=MGH). The total energy would be the kenetic plus potential energy. As the height increases, the energy increases. Should there be a constant increase between the crater depth with each drop?

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# Homework Help: Crater Depth and Height Relationship

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