Calculating Equations of Impact for a Chain of Links | Homework Help"

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In summary, the conversation discussed a problem involving calculating the equations of impact for a chain of links and determining the joint velocities of the links after impact. The person had attempted to solve the problem without a dependent variable, but was unsure of how to incorporate it. They shared their attempt in a PDF file and asked for help. The conversation also mentioned relevant equations and a possible solution.
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J1986
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Homework Statement



Hello!

I have a problem to calculate the equations of impact (not elastic) of a chain of links.
The goal is to have joint velocities of the links after impact.

I know how to do this without a dependent variabele, see my attempt in
http://student.vub.ac.be/~jdhoker/Equations_of_impact.pdf

But I have no idea how to incorporate the dependent unknown. Any ideas are welcome!


Homework Equations



All info and relevant equations are also in the file because I'm not familiar with Latex.

The Attempt at a Solution



The attempt is also in the pdf.

Thanks!
J
 
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Can this be a solution? But I'm very unsure about it...

I've tried to describe that the joint velocities variation is dependent on multiple links.

[PLAIN]http://student.vub.ac.be/~jdhoker/solution.jpg

Please help :-) !
 
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1. How do I calculate the equation of impact for a chain of links?

To calculate the equation of impact for a chain of links, you will need to follow these steps:

  • 1. Determine the mass and velocity of each link in the chain.
  • 2. Calculate the kinetic energy of each link using the equation KE = 1/2 * mass * velocity^2.
  • 3. Add up the kinetic energy of each link to get the total kinetic energy of the chain.
  • 4. Use the equation of conservation of energy (KE + PE = constant) to calculate the potential energy of the chain.
  • 5. Finally, use the equation of impact (m1v1 + m2v2 = (m1 + m2)v') to calculate the velocity of the chain after impact.

2. What is the equation of impact used for?

The equation of impact is used to calculate the velocity of an object after a collision or impact. It takes into account the masses and velocities of the objects involved, and is based on the principle of conservation of momentum.

3. Is there a specific formula for calculating the equation of impact?

Yes, the general formula for calculating the equation of impact is m1v1 + m2v2 = (m1 + m2)v', where m1 and m2 are the masses of the objects, v1 and v2 are their velocities before impact, and v' is their combined velocity after impact.

4. Can the equation of impact be used for non-rigid objects?

Yes, the equation of impact can be used for both rigid and non-rigid objects. However, in the case of non-rigid objects, the calculation may be more complex as the objects may deform or change shape upon impact, affecting their masses and velocities.

5. Are there any limitations to using the equation of impact?

The equation of impact can only be used for collisions or impacts where momentum is conserved. This means that the objects involved must not experience any external forces during the impact. Additionally, the equation may not be accurate for highly elastic collisions, where some of the kinetic energy is converted into potential energy instead of being conserved.

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