Kinetic Energy, Density and distance embedded

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Discussion Overview

The discussion revolves around the relationship between kinetic energy, density of materials, and the distance a projectile embeds into various surfaces upon impact. It explores theoretical and practical considerations regarding impacts at different velocities and material properties.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about a formula that accounts for kinetic energy, density, and embedding distance of a projectile into different surfaces.
  • Another participant suggests that for large velocities, the embedding distance could be approximated by the length of the projectile multiplied by the density ratio of the projectile to the surface material, while noting the importance of shape and material constants.
  • There is a question regarding the classification of large velocity impacts, whether defined by a specific velocity or a percentage of terminal velocity.
  • Another participant proposes that the velocity after impact could be considered as zero relative to the target, hinting at material constants' relevance.
  • One participant emphasizes the distinction between local and widespread damage based on the impact speed and material properties, suggesting that dimensional analysis may reveal a critical dimensionless value involving density, impact speed, and tensile strength.

Areas of Agreement / Disagreement

Participants express differing views on the classification of large velocity impacts and the factors influencing embedding distance, indicating that multiple competing perspectives remain without a consensus.

Contextual Notes

Participants acknowledge the complexity of the problem, noting that there may not be a universal formula that encompasses all relevant effects, and that material constants and impact characteristics play significant roles.

MikeyBear
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A projectile hits different surfaces, each time the projectile has varying kinetic energy values, the surfaces also have varying densities. Is there any formula that accommodates for these variables in terms of the distance the projectile embeds into the surface?
 
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For large velocities, the distance should be approximately given by the length of the projectile, multiplied by the density ratio of the projectile relative to the surface material (I am too lazy to look for a source). However, the shape and some material constants can be important, too. I don't think there is a universal formula which can cope all relevant effects.
 
Are large velocity impacts classified by a certain velocity or by a percentage of an objects terminal velocity?
 
By something related to material constants. The velocity after the impact (and relative to the target) is 0?
 
MikeyBear said:
Are large velocity impacts classified by a certain velocity or by a percentage of an objects terminal velocity?

It matters whether the damage is local or widespread. A low speed impact on a strong lightweight material will deform a wide area. That spreads the absorption of energy and limits the peak damage. Impact into a very weak material, like soft earth, will hardly be spread at all. At high speeds into a dense material, the inertia of the surrounding material may prevent spreading, leading to a neat, deep hole.
Dimensional analysis suggests the dimensionless value R.V[itex]^{2}[/itex]/T (R = density, V = impact speed, T = tensile strength) may be critical.
 

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