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

ar202

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

tiny-tim

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!

ar202

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...

tiny-tim

Hi ar202!

erm … you keep writing 4 instead of 3 …

ar202

haha so i have :p

the answer is still wrong... any tips?

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?)

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.

tiny-tim

Well, then they're obviously going in the same direction originally …

relative speed before = 1, after = 0.4

ar202

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...?

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.

ar202

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

tiny-tim

oooh, i see it now …
… there's no "X 2" …

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

ar202

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

tiny-tim

(just got up …)

oh, it multiplied the whole equation!

ok, then your 18 should be 16.8

ar202

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!!

tiny-tim

you do know that 15.2/6=2.53333333333 ?