Finding the Speed of a System of Three Bodies Before Collision

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Discussion Overview

The discussion revolves around a problem involving a system of two identical spheres and a mobile platform, focusing on determining the speed of each sphere just before they collide. The problem is approached from various angles, including conservation laws and equations of motion, and is framed as a challenge problem created by one of the participants.

Discussion Character

  • Homework-related
  • Debate/contested
  • Exploratory

Main Points Raised

  • One participant suggests that the problem can be solved using the conservation of potential energy converting to kinetic energy.
  • Another participant argues that additional equations are necessary beyond conservation laws, indicating that momentum conservation alone is insufficient.
  • Some participants express skepticism about the ease of the problem, suggesting it requires more complex analysis, such as writing equations of motion for all bodies involved.
  • A participant proposes starting with simpler scenarios, such as a single ball on a slope, to build up to the original problem.
  • One participant indicates that they created the problem themselves and seeks opinions from specialists on potential solutions.
  • Another participant suggests that the problem might be too complex for the intended level of study and encourages seeking guidance from the source of the problem.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the approach to solving the problem, with multiple competing views on the sufficiency of conservation laws and the complexity of the required analysis.

Contextual Notes

Participants express uncertainty about the appropriate methods to apply, with some suggesting that the problem's complexity may exceed typical homework expectations. There are references to the need for additional equations and the potential for different limits in the equations of motion.

Who May Find This Useful

Individuals interested in mechanics, particularly those dealing with systems of bodies and conservation laws, may find this discussion relevant.

orlan2r
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The figure shows a system consisting of two identical spheres of mass m and a mobile platform mass M. If the system starts from rest in the position shown in the figure, what is the speed from each sphere in the moment when both move horizontally, before the crash occurs. Neglect all friction.
 

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This looks lie a homework type question. Easy(ish) to solve if you remember that the PE at the start becomes KE at the end.
 
Its not easy. Please try it to solve
 
orlan2r said:
Its not easy. Please try it to solve
I will have a go this evening if time permits. Is it really not just the conservation laws that solve it? (Momentum too)
 
sophiecentaur said:
I will have a go this evening if time permits. Is it really not just the conservation laws that solve it? (Momentum too)
NO
more equation is needed
 
orlan2r said:
NO
more equation is needed
What else equations? It is obvious that Newtonion physics is sufficient... you have not even friction!
 
Omega0 said:
What else equations? It is obvious that Newtonion physics is sufficient... you have not even friction!
Conservation of momentum on the x-axis and conservation of energy (2 equations but three unknown speeds)
 
orlan2r said:
Conservation of momentum on the x-axis and conservation of energy (2 equations but three unknown speeds)
Yep. Fair enough. Another equation is needed too.
 
sophiecentaur said:
I will have a go this evening if time permits. Is it really not just the conservation laws that solve it? (Momentum too)
Can you help me sophiecentaur?
 
  • #10
Someone who can help me in this challenge problem?
 
  • #11
orlan2r said:
Can you help me sophiecentaur?
Sorry about this but it requires a lot of time, I think. Afaics, you would need to write out the equation of motion, from t = 0, for all three bodies and arrive at an integral which has to be solved. To make it harder, the limits for the short fall will be different from the long fall.
BTW, who has set you this beastly problem? Perhaps you could go back and ask for guidance? After all, they really should be able to help - if they have actually realized how hard the problem appears to be. Is it a a level that's appropriate to the level of the course you're following?
 
  • #12
This problem I have created myself. Who do you think could help me?
 
  • #13
orlan2r said:
This problem I have created myself. Who do you think could help me?
If it your own problem then perhaps you should start from the beginning, with a simpler situation and work up to your OP.
Start with a single ball on a linear slope, then a single ball on a circular slope.
PF has had a number of threads about blocks on inclined planes (fixed and sliding), to give you a start with finding the sort of approach needed.
 
  • #14
sophiecentaur said:
If it your own problem then perhaps you should start from the beginning, with a simpler situation and work up to your OP.
Start with a single ball on a linear slope, then a single ball on a circular slope.
PF has had a number of threads about blocks on inclined planes (fixed and sliding), to give you a start with finding the sort of approach needed.
AlreadyI did it. Only I wish to know the opinion of a specialist.
Could you propose this problem on other forum please. I can`t believe that nobody can propuse a solution.
Thanks
 

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