## Momentum + coefficient of restitution this is driving me nuts!!!

1. The problem statement, all variables and given/known data

A Mass of 2kg travelling at 2m/s is struck by a mass of 4 kg travelling at 3m/s. If the coefficient of restitution for the two materials is 0.4 calculate their final velocities.

2. Relevant equations

M1U1+M2U2=M1V1+M2V2

E=V2-V1/U2-U1

3. The attempt at a solution

From what i know, the best way to do it is use both equations and create two simultaneous equations?

Is this correct? i seem to end up with V2=-1.2 however im pretty sure this is wrong.

any help would be great.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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 Quote by ar202 A Mass of 2kg travelling at 2m/s is struck by a mass of 4 kg travelling at 3m/s. If the coefficient of restitution for the two materials is 0.4 calculate their final velocities. … i seem to end up with V2=-1.2 however im pretty sure this is wrong.
Hi ar202! Welcome to PF!

Show us your full calculations, and then we'll see what went wrong, and we'll know how to help!

 Cheers dude :-) first bit... 2*2+4*(-4)=2*V1+4*V2 -12=2*V1+4*V2 second bit... 0.4*2-0.4*4=v2-v1 2.4=v2-v1 so then i have -12=2*V1+4*V2 + 4.8=2V2-2V1 which gives -7.2=6V2...

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## Momentum + coefficient of restitution this is driving me nuts!!!

Hi ar202!

erm … you keep writing 4 instead of 3 …
 Quote by ar202 A Mass of 2kg travelling at 2m/s is struck by a mass of 4 kg travelling at 3m/s. If the coefficient of restitution for the two materials is 0.4 calculate their final velocities.
 Quote by ar202 2*2+4*(-4)=2*V1+4*V2 … 0.4*2-0.4*4=v2-v1

 Quote by tiny-tim Hi ar202! erm … you keep writing 4 instead of 3 …
haha so i have :p

the answer is still wrong... any tips?

 Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor Have you checked that your signs for V1 and V2 are the right way round in both equations? (and btw, were they travelling in the same direction originally, or in opposite directions?)

 Quote by tiny-tim Have you checked that your signs for V1 and V2 are the right way round in both equations? (and btw, were they travelling in the same direction originally, or in opposite directions?)
it doesn't mention directions, just that it is struck. I've found the answers - V1=2.53 & V2=2.93

still struggling to get to those answers.

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 Quote by ar202 it doesn't mention directions, just that it is struck. I've found the answers - V1=2.53 & V2=2.93 still struggling to get to those answers.
Well, then they're obviously going in the same direction originally …

relative speed before = 1, after = 0.4

 Quote by tiny-tim Well, then they're obviously going in the same direction originally … relative speed before = 1, after = 0.4
Ok so using the same method as before i can get V2=2.83 & V1=2.34

am i going about it the right way...?

 Blog Entries: 27 Recognitions: Gold Member Homework Help Science Advisor hmm … relative speed after = 0.49 … not close enough to 0.4 you must be making a mistake somewhere, but without seeing the details, I can't say where.

 Quote by tiny-tim hmm … relative speed after = 0.49 … not close enough to 0.4 you must be making a mistake somewhere, but without seeing the details, I can't say where.
first part

2*2+4*3=2*v1+4*v2

0.4(3-2)=v2-v1 X 2 then i've added it to the first part...

so 18=6*v2

18/6=3 .... actually my answer was 3 for v2. I must be more tired than i thought :p

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oooh, i see it now …
 Quote by ar202 0.4(3-2)=v2-v1 X 2
… there's no "X 2" …

the coefficient of restitution is just |u1 - u2|/|v1 - v2|

 the 'X2' was the simultaneous equation part...

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 Quote by ar202 the 'X2' was the simultaneous equation part...
(just got up …)

oh, it multiplied the whole equation!
ok, then your 18 should be 16.8

 Quote by tiny-tim (just got up …) oh, it multiplied the whole equation! ok, then your 18 should be 16.8

ok i finally got there

got it down to 6v2=15.8

15.8/6=2.53333333333

thanks for your help dude. think i made it alot harder than it should have been!!

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