D’Alambert vs Newton’s second law?

[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?

 

[Dr.D]

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?

 

[Jon1909]

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?

 

[Jon1909]

Ma being mass x acceleration and mgh being mass x gravity x height

 

[Dr.D]

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.

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?