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Couple of M2 collisions qus watch

1. Hi, chapter 4 of M2 book, ex 4B qu 5 and 7 - im stuck

5) 2 particles collide, one 3kg 8m/s, other 12 kg at rest. The travel opposite directions after collision, find inequality satisfied by e.

7) A sphere of mass m is moving with a speed V along a horizontal straight line. It collides with an identical sphere of masss m moving along the same straight line in the same direction with speed u (u<V) Show that the magnitude of the impulse on either of the speres is
1/2m(1+e)(V-u)
where e is the coefficient of restitution between the two spheres.

The answer to 5 is e>0.25, I have the same problem with both questions - I have lots of unknowns and no matter how many simultaneous equations I have, I cant seem to emilinate them

thanks,
franks xxx
2. Conservation of momentum;

24 + 0 < 12u

2 < u

also

8e > u

so 8e > 2 , the inequality follows

For the first inequality, we know that the resultant momentum is going to be 12u - 3v , since the first particle will rebound, will be travelling in negative direction. so if 12u - (positive quantity) = 24 , then 12u >24

For the second inequality, we have e = v+u /8

8e = v + u

do the same thing, u must be less than 8e since v is a positive value
3. 24 + 0 < 12u

2 < u

also

8e > u

so 8e > 2
where did you get that from, and how did you get rid of v's, my conservation of momentum eqn was:
24 = 12v2 - 3v1
 what does your u stand for?
4. my u stands for your v2

yes you have 24 = 12u - 3v , what does this tell you about the size of 12u, is it larger or smaller than 24?
5. larger... ok so I understand 12u > 24 so u > 2 Im working on the rest....
6. thanks, I think I get it !! Any ideas about the 2nd qu?!
7. (Original post by franks)
7) A sphere of mass m is moving with a speed V along a horizontal straight line. It collides with an identical sphere of masss m moving along the same straight line in the same direction with speed u (u<V) Show that the magnitude of the impulse on either of the speres is
1/2m(1+e)(V-u)
where e is the coefficient of restitution between the two spheres.
mV + mu = mv1 + mv2 => V+u = v1+v2 (1)
e = (v2-v1)/(V-u)
=> v2-v1 = e(V-u) (2)

(1)+(2)
2v2 = e(V-u) + V+u
=> v2 = 0.5e(V-u) + 0.5(V+u)

Impulse exerted on sphere
= m(v2-u)
= m(0.5e(V-u) + 0.5(V+u) - u)
= 0.5m(e(V-u) + V-u)
= 0.5m(1+e)(V-u)
8. thank you I'll try and rep you, may not be worth anything though!

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