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Oblique Impact Between Two Smooth Spheres

I could prove the expression for J in this question, and I got the value of delta using the general equation of the kinetic energy of a body. But I want to know how to get the same answer by considering the impulse. And I think I'm stuck at there. If someone can help me to solve that part and also the last two parts, It is really appreciated...

Reply 1

DFranklin

Answering this from scratch is going to be rather a lot of work (that I don't really feel like doing). Some thoughts:

I can't see how knowing the impulse is going to help (i.e. I think you're basically going to end up calculating the K.E. whatever you do).

If A has velocities x1, y1 parallel/perpendicular to the line of centres before the collision, and velocities x2, y2 after the collision (in the same directions), then the angle of deflection is going to be arctan(y2/x2) - arctan(y1/x1). But then you can calculate the tangent of this using the formula for tan(A - B) (and y1/x1 is going to = t, and you can also work out y2/x2 in terms of t). It will probably need a bit of algebra bashing, but I wouldn't expect it to be too bad.

For the last part, T is going to be maximised when (1+e)/T is minimized, and the other side of that expression is just a function of t, so you can find the value of t that minimizes it.

If you're still stuck and you post your working, I might have a look, but I make no promises (these questions are rather tedious IMHO).