# FM1 question

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#1
Hii please could someone help me with part b
thank youu
Last edited by Qxi.xli; 1 month ago
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#2
I'm just getting confused because e<0<=1 and we're told that 0<lambda<1/2, and I don't know which one I'm supposed to use, if that makes sense?
Last edited by Qxi.xli; 1 month ago
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1 month ago
#3
(Original post by Qxi.xli)
I'm just getting confused because e<0<=1 and we're told that 0<lambda<1/2, and I don't know which one I'm supposed to use, if that makes sense?
can you post what you've tried?
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#4
(Original post by Muttley79)
can you post what you've tried?
I mean I've tried equating the answer from part a, but it just turned into a mess and I wasn't getting anywhere near the answer.
how would I start it?
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1 month ago
#5
(Original post by Qxi.xli)
I mean I've tried equating the answer from part a, but it just turned into a mess and I wasn't getting anywhere near the answer.
how would I start it?
Just do conservation of momentum equation and e x approach speed = separation speed

I got (a) from these. then use the restrictions ...
Last edited by Muttley79; 1 month ago
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#6
(Original post by Muttley79)
Just do conservation of momentum equation and e x approach speed = separation speed

I got (a) from these.
oh I've got the answer to part a, I'm stuck on b?
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1 month ago
#7
(Original post by Qxi.xli)
oh I've got the answer to part a, I'm stuck on b?
I edited my post - I rearranged the expression for e to get k.
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#8
(Original post by Muttley79)
I edited my post - I rearranged the expression for e to get k.
which restrictions do I use?
there are two? e<0<=1 and 0<lambda<1/2? Do I need to use both? If so which one should I start with?
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1 month ago
#9
(Original post by Qxi.xli)
which restrictions do I use?
there are two? e<0<=1 and 0<lambda<1/2? Do I need to use both? If so which one should I start with?
Well you want to find the minimum value of k, if that helps?
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1 month ago
#10
(Original post by Qxi.xli)
which restrictions do I use?
there are two? e<0<=1 and 0<lambda<1/2? Do I need to use both? If so which one should I start with?
I used e as I said and got an inequality for k - it might not be the only approach
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#11
(Original post by laurawatt)
Well you want to find the minimum value of k, if that helps?
no, still confused lol
i mean λ<1/2 is the smallest?
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#12
(Original post by Muttley79)
I used e as I said and got an inequality for k - it might not be the only approach
ok thanks, but if you had used the other inequality and got the correct answer, would you still get all the marks? x
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1 month ago
#13
(Original post by Qxi.xli)
ok thanks, but if you had used the other inequality and got the correct answer, would you still get all the marks? x
Getting an expression for e seems the logical approach as you've done that for (a) - I haven't tried getting an expression for lambda but it looks more tricky
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#14
(Original post by Qxi.xli)
which restrictions do I use?
there are two? e<0<=1 and 0<lambda<1/2? Do I need to use both? If so which one should I start with?
mqb2766 ^ sorry for tagging you, please could you help😭 I just keep getting questions like these wrong ):
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1 month ago
#15
(Original post by Qxi.xli)
mqb2766 ^ sorry for tagging you, please could you help😭 I just keep getting questions like these wrong ):
What do you get when you rearrange the inequality
e < 1
In terms of k?

Note, your original e < 0 < 1 isn't right as I'm sure you realize, it should be 0 < e < 1. The 0 < e is trivially satisfied (the numerator & denominator is positive) so just consider e < 1.
Last edited by mqb2766; 1 month ago
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#16
(Original post by mqb2766)
What do you get when you rearrange the inequality
e < 1
In terms of k?

Note, your original e < 0 < 1 isn't right as I'm sure you realize, it should be 0 < e < 1. The 0 < e is trivially satisfied (the numerator & denominator is positive) so just consider e < 1.
that gives 1<k(-2λ +1)

oh yeah sorry, that was a typo.
so in questions like this, we always ignore the 0<e?
because if I had re-arranged e>0, it gives that gives kλ>-1. Isn't that important information? idk
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1 month ago
#17
(Original post by Qxi.xli)
that gives 1<k(-2λ +1)

oh yeah sorry, that was a typo.
so in questions like this, we always ignore the 0<e?
because if I had re-arranged e>0, it gives that gives kλ>-1. Isn't that important information? idk
Thats (both) correct. For e > 0, k and lambda are both > 0, so
k*lambda > 0 > -1
So trivially satisfied, so not important for this question.

Note that when lambda=0, e=1 and k=1, this was essentially a Newton's cradle question where a moving ball collides with a stationary, identical ball and the first ball is brought to a complete halt and transfers all its velocity to the second ball. This is the scenario that gives the k=1 condition.
Last edited by mqb2766; 1 month ago
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#18
(Original post by mqb2766)
Thats (both) correct. For e > 0, k and lambda are both > 0, so
k*lambda > 0 > -1
So trivially satisfied, so not important for this question.

Note that when lambda=0, e=1 and k=1, this was essentially a Newton's cradle question where a moving ball collides with a stationary, identical ball and the first ball is brought to a complete halt and transfers all its velocity to the second ball. This is the scenario that gives the k=1 condition.
hang on sorry where did you get this from?

ohh wow nice that's cool
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#19
(Original post by mqb2766)
Thats (both) correct. For e > 0, k and lambda are both > 0, so
k*lambda > 0 > -1
So trivially satisfied, so not important for this question.

Note that when lambda=0, e=1 and k=1, this was essentially a Newton's cradle question where a moving ball collides with a stationary, identical ball and the first ball is brought to a complete halt and transfers all its velocity to the second ball. This is the scenario that gives the k=1 condition.
Also, what do I do after that bit? where do I use this 0<lambda<1/2 lol😭
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1 month ago
#20
(Original post by Qxi.xli)
Also, what do I do after that bit? where do I use this 0<lambda<1/2 lol😭
What did you get as your inequality for k? Then you use the lambda part .... post your working.
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