Calculating Spherical Collision Outcomes

[Badmachine]

A spherical mass (m1 at 4 kilograms), moving at 10m/s from the northwest (or from the direction of 315 degrees), collides with another spherical mass (m2 at 2 kilograms), moving at 5m/s from the south (or from the direction of 180 degrees).

Mass m2 is now redirected toward the southwest (or towards the direction of 225 degress).

How would one calculate for the new direction of m1?

Thank you.

P.S.: Not homework.

 

[jtbell]

Assuming the collision is elastic, so kinetic energy is conserved...

You set up equations for conservation of energy, conservation of x-component of momentum, and conservation of y-component of momentum. This gives you three equations which you can solve for the three unknowns: speed of m1, speed of m2, and direction of m2.

Even though this may not be an actual homework question, it is a homework-like question, and therefore belongs in the homework forums (and has been moved there.)

 

[Badmachine]

Thanks JTB.

Two other questions if I may:

- Would a change in velocity of m1 or surface friction coefficients of m1 and m2, result in a deflection angle change for m1?

- Could this same model be used to calculate an aircraft deflection angle created by a crosswind, if aircraft speed, air density and air velocity are known? (ordinary "wind triangle" calculations don't seem to account for this question when different speeds are applied)

E.g.: an aircraft would become m1 (same direction) and a crosswind would become m2 (same direction).

 

[jtbell]

OK, I thought you wanted to work out the solution for that particular situation, which is why I moved this originally to the homework forums. Simple collisions like the one you described are pretty common homework exercises in introductory physics courses. Now it appears you want to discuss this more generally, so I've moved it back to the original forum. Sorry for the confusion.

- Would a change in velocity of m1 or surface friction coefficients of m1 and m2, result in a deflection angle change for m1?

A change in v1 would make a difference, in general.

Friction between m1 and m2 would in general cause both spheres to start rotating (if they weren't rotating to begin with) or change their state of rotation. If their rotational kinetic energy is significant (compared to their translational kinetic energy) you'd have to take that into account in energy conservation. I've never tried to solve a problem like that myself.

- Could this same model be used to calculate an aircraft deflection angle created by a crosswind, if aircraft speed, air density and air velocity are known? (ordinary "wind triangle" calculations don't seem to account for this question when different speeds are applied)

I doubt this would work very well. This sounds like a rather complex aerodynamic problem. You've got bazillions of air molecules (not a single rigid object) colliding with the plane and with each other. The motions of the molecules are affected by the motions of the other molecules (fluid flow).