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M3 Question Help, Oblique Collisions (AQA) Watch

1. hello,
I've been stuck on the first part of this question for quite sometime. Ive done the second part funnily enough, its easier than the first.

A small sphere A of mass m collides obliquely with
an identical sphere also of mass m. The spheres are
perfectly elastic (e = 1).
Show that the paths of the two spheres after collision
are at right angles.
Prove that there is no loss in kinetic energy.

I tried to come up with general vectors for the velocity of A and B and quite a few things. Which led me to things like
UA=pcos(x) i + psin(x) j
UB=qcos(y) i + qsin(y) j

using conservation of momentum and newton's experimental law of restitution I would arrive to something of the form.

VA= qcos(y) i + psin(x) j
VB= pcos(x) i + qsin(y) j

I would then work out the tan of their new directions. But that didn't help very much in giving me an idea of how to show the angles are perpendicular.

If we call the new direction direction of A, A' and of B, B'.
. hhmm I think i see where im going wrong....Ill try again
Id appreciate any help still
Thanks
2. (Original post by jarasta)
Id appreciate any help still
Thanks
Firstly, I'd check the question again. I suspect that the second sphere is initially at rest.
3. (Original post by ghostwalker)
Firstly, I'd check the question again. I suspect that the second sphere is initially at rest.
Aaahh that simplifies the problem greatly if that is so.
It says,
A sphere collides obliquely with a second, identical sphere. The Collision is perfectly elastic.
Show that....

Is it implied?
4. (Original post by jarasta)
Aaahh that simplifies the problem greatly if that is so.
It says,
A sphere collides obliquely with a second, identical sphere. The Collision is perfectly elastic.
Show that....

Is it implied?
It's not really implied, but what you're trying to show is only true if the second sphere is stationary. Badly worded question, IMHO.

Also, I'd assign one of your axes along the line of centres (with the other at right angles to it), makes the calculation even easier.
5. (Original post by ghostwalker)
It's not really implied, but what you're trying to show is only true if the second sphere is stationary. Badly worded question, IMHO.

Also, I'd assign one of your axes along the line of centres (with the other at right angles to it), makes the calculation even easier.
Alright, ill try that. Thank you!

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