How Can Rectangular Prisms Transform Billiards?

MenhirMetonym
Messages
1
Reaction score
2
Homework Statement
Consider a rectangular prism struck by a cue, what are the resulting dynamics if the object has two continuous mass distributions and the base height is longer than the top height?
Relevant Equations
Impulse, Torque, Total Energy, and Euler-Lagrange.
I plan to add on to this as I have time and ability. Apologies for the weird formatting.
1687908688639.png

COM_diagram.png
diagrm2.png


1687908738625.png

1687908113303.png

1687908173840.png
 

Attachments

  • 1687908138005.png
    1687908138005.png
    59.3 KB · Views: 111
Physics news on Phys.org


No need to apologize for the formatting, we're all here to share our ideas and improve together! Your idea of using rectangular prisms for a game of billiards is quite interesting. It would definitely add a new twist to the traditional game. I can imagine the challenge of calculating the angles and trajectories of the balls bouncing off the different edges of the prisms.

I'm curious to know how you plan on incorporating the rectangular prisms into the game. Will they serve as the pockets or will they be used as obstacles on the table? Either way, it would definitely require some strategic thinking and precise aiming skills.

I also think it would be great to see different sizes and shapes of rectangular prisms used in the game. This would add another layer of complexity and make it even more challenging. And as you mentioned, adding on to this idea with more time and ability would definitely make it even more exciting.

Overall, I think incorporating rectangular prisms into billiards is a unique and creative idea. I look forward to seeing how you develop it further and potentially trying it out myself. Keep exploring and experimenting, that's how great ideas are born!
 
Thread 'Need help understanding this figure on energy levels'
This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
Thread 'Understanding how to "tack on" the time wiggle factor'
The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
Back
Top