Conservation of Momentum 2D Collision angles/directions

[Ocata]

Hi,

I googled 2d elastic collisions to see if I could find a problem where two objects are approaching each other from different directions before collision and then moving away from each other at different directions after collision, but I noticed that all the problems I've found have 1 of two scenarios:

Approaching each other in a linear fashion before collision and then moving away from each other after collision at different angles.

Or approaching each other from different directions/angles before collision and then both objects move in the same direction after collision in an inelastic way.

So how come I haven't noticed any problems where each object has different angles/directions both before and after collision?

 

[gsal]

I am not sure I follow. Isn't the first scenario that you presented applicable to any incoming angle? I am thinking the trig should be the same.
By the way in your first scenario, what did you mean by approaching in linear fashion? Collinear? If so, how come they move away in different angles?

 

[dennisron]

Momentum is a vector and as with any vector, it can be resolved into components. Generally, we resolve vectors into horizontal (x) and vertical (y) components. The diagram to the right shows a vector, v, resolved into its x and y components. Momentum is "mass in motion", or a measure of how much motion an object has.

 

[A.T.]

So how come I haven't noticed any problems where each object has different angles/directions both before and after collision?

You can transform any problem into a reference frame where this is the case.

 

[Ocata]

qsal, dennisron, and A.T.,

Okay, thanks, I'll go ahead and give it a try. I'll make up a problem and try solving it up until the point where I believe I'll be getting stuck and post it in the HW section for further evaluation and guidance. Thank you.

 

[Nidum]

The analysis of two balls with different approach angles and velocities rebounding after collision is very complex .

In general the balls could contact each other anywhere on the approach sides of their profiles ( actually could miss altogether in many cases) .

Rebound angles then depend on the angles of approach and on angles of contact on the two spherical profiles . Also any significant off set of contact points relative to ball centres can cause spin which can alter the rebound angles and in some cases cause ball to track away on a curved path .

Study the kinetics of ball contact in table games such as Billiards and Snooker . Even though there is now one static target ball and one moving cue ball many of the principles are the same as for two balls moving . Expert players exploit the advantages of offset contact collisions . Indeed they take things further by not only offsetting the contacts but also adding side and/or top spin to cue ball when taking shot .

 

[Ocata]

Thank you Nidum,

The scenario I'm presenting is actually not intending to take into account a lot of the (necessary) parameters you have described for sake of beginner simplicity. I'm just looking at the problem from the perspective described in a basic, high school level, non calculus, applied physics type of textbook.