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Why is this >0 but not >= 0 ?

FMechanics, the question in my next comment (TSR really need to let us embed images on thread-openers), question B has the answer
0 < e < 2/5

I got the < 2/5 part. This was very well understood. I am entirely lost with how > 0 is achieved. I would understand >= 0, as, 0 <= e <= 1 but this was not the case in this Q. Is the markscheme wrong?

I also substituted e = 0 into the question, which they coalesce. If the two particles are travelling together with the same velocity, is e >0 because they don't technically "collide" again? and that they're a part of the same "system"?

Many thanks.

Reply 1

The stupid website does not let me even attach in comments! (gives an error). I will probably use reddit in future. Shame.

The question is here, Question paper - 9FM0-3C A Level Further Mechanics 1 - June 2022
Question 5b.

Reply 2

Original post
by hwhejfjejsjx
FMechanics, the question in my next comment (TSR really need to let us embed images on thread-openers), question B has the answer
0 < e < 2/5
I got the < 2/5 part. This was very well understood. I am entirely lost with how > 0 is achieved. I would understand >= 0, as, 0 <= e <= 1 but this was not the case in this Q. Is the markscheme wrong?
I also substituted e = 0 into the question, which they coalesce. If the two particles are travelling together with the same velocity, is e >0 because they don't technically "collide" again? and that they're a part of the same "system"?
Many thanks.

Sure, if e=0 they dont collide a second time as theyre part of the same system.

Reply 3

Original post
by mqb2766
Sure, if e=0 they dont collide a second time as theyre part of the same system.

Okay great, my thinking was correct, I just wanted to confirm. Thankyou

Reply 4

Original post
by hwhejfjejsjx
Okay great, my thinking was correct, I just wanted to confirm. Thankyou

Yes. Not sure what you did or the mark scheme says, but a back of the envelope would say that Q must change direction in the collision so the only way there wouuldnt be a second collision would be

If P is moving away from the wall faster than Q (after the wall rebound). P would reverse direction of motion in the initial collision.

If P joins with Q in the collision (as if theyre heading in the same direction Ps post collision speed must <= Qs)

Otherwise the post collision velocity is fairly irrelevant and a second collsiion with Q will happen. A sketch can help. Then its just a matter of a few linear equations/inequalities to sort it out.
(edited 11 months ago)

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