D’Alambert vs Newton’s second law?

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Discussion Overview

The discussion revolves around the differentiation between D'Alambert's principle and the conservation of energy in the context of calculating the average resistance of the ground after an object strikes it. Participants are exploring the application of these concepts to a specific problem involving a mass dropped from a height and its interaction with the ground.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant presents an equation, Ma + Mgh - Fr = 0, but lacks clarity on the definitions of variables and the concept of resistance.
  • Another participant questions the clarity of the initial question and seeks definitions for terms like "M," "h," and "resistance," suggesting that the problem lacks specificity.
  • A level 3 student expresses difficulty in distinguishing between D'Alambert's theory and the conservation of momentum, indicating that the question is poorly framed and lacks real-life context.
  • Participants discuss the implications of different ground properties on the resistance experienced, noting that materials like sand and granite may yield different results.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the clarity of the problem or the correctness of the proposed equation. Multiple competing views remain regarding the definitions and applications of the concepts involved.

Contextual Notes

The discussion highlights limitations in the problem statement, including vague definitions and the absence of necessary real-life information that would aid in formulating a clearer question.

Jon1909
I’m a bit stuck with differentiating between the conservation of energy and D’Alambert. For a question I need to find the average resistance of the ground after it has been struck by an object. I chose to look at the equation as Ma + Mgh - Fr = 0.

Can you advise if this is correct?
 
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You really have not stated a clear question. In your equation, what is M? what is h? What do you mean by resistance (resistance to penetration), resistance to returning to the previous local shape, etc. What are you really trying to accomplish here?
 
Ok so I’m currently a level 3 student. The question I’ve been looking at is very difficult to answer because it is very poor.

I’ve been asked to solve a question in 2 separate ways. Using D’Alambert’s theory and using the conversation of momentum.

I have got an answer I am happy with for the momentum but for D’Alambert, I am struggling to differentiate between that and the conversation of energy.

The question is at best specious, lacking real life information (that would make the question much more pertinent and answerable)

I am trying to find the average resistance of the ground when a mass is dropped from a certain height onto another mass, causing the combined mass to move a certain amount into the ground... does that help?
 
Ma being mass x acceleration and mgh being mass x gravity x height
 
Jon1909 said:
Ma + Mgh - Fr = 0.

I think I can say with confidence that your equation above is not correct, even though the problem is still not at all clear.
Jon1909 said:
I am trying to find the average resistance of the ground when a mass is dropped from a certain height onto another mass, causing the combined mass to move a certain amount into the ground... does that help?

What are you going to say about the properties of the ground? A surface of sand will probably behave differently from a granite surface. Are you concerned only with the depth of the indentation, or do you want to describe rebound, or what?
 

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