Elastic collisions inside a hollow cilinder

[gabrielbhl]

Hi everybody.
That's my first (of many) post here!
I'm a brazilian guy who is trying o solve de Wopho's Problems.
And onde of then called my attention for the criativity using an (theoterically) easy concept of elastic collision.
The problem is the second http://wopho.org/selection-downloadproblem.php?id=3

I have an hollow cylinder and an disc inside it with V_o and I (and the problem) ask you what wiil happens after de collisions (that is: the velocity of the disc and cylinder after the first e nth collision)
I'm really needing some help in this excellent problem, but that is not my homework, and yes a good problem which requires reasonig.
Any idea??

Thank's for the attention and sorry for my bad english!

 

[gabrielbhl]

I've tryied using theta=0 and then put some sen and cos but I failed!



In my opinion, that is the best collision problem ever

 

[gabrielbhl]

Anyone?? Please i need your help!

 

[nekronaut]

"The competition is for individuals, solutions sent by group of students are not accepted.

All participants must solve the problems individually. The problems can be downloaded from the problem section of the WoPhO Selection Round webpage"

 

[PJC01]

Hello!

First of all, welcome to the community and good luck with solving the Wopho's Problems! It's great to see someone interested in using creativity to solve problems.

Now, for your question about elastic collisions inside a hollow cylinder, let's break it down step by step. First, let's define what an elastic collision is. It is a collision between two objects where the total kinetic energy of the system is conserved. This means that the total energy before the collision is equal to the total energy after the collision.

In the problem given, we have a hollow cylinder and a disc inside it, both with initial velocities. The first thing we need to consider is the conservation of momentum. Since there are no external forces acting on the system, the total momentum before the collision should be equal to the total momentum after the collision. This means that the sum of the mass of the cylinder and the disc multiplied by their respective velocities should be the same before and after the collision.

Now, let's consider the elastic collision between the two objects. During the collision, both the cylinder and the disc will experience a change in velocity. However, since it is an elastic collision, the total kinetic energy of the system should remain the same. This means that the total kinetic energy before the collision should be equal to the total kinetic energy after the collision. This can be represented mathematically as 1/2 * m * v^2 = constant.

Using these principles, you can solve for the velocities of the cylinder and the disc after each collision. Just remember to take into account the conservation of momentum and the conservation of energy.

I hope this helps you with solving the problem. Keep using your creativity and reasoning skills, and you'll be able to find the solution. Good luck!