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Applied maths: Help needed

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Comments

  • #32
    Mutant_Fruit
    Closed Accounts Posts: 4,943 ✭✭✭Mutant_Fruit


    what are the laws governing the oblique collision of two spheres?


  • #33
    PrecariousNuts
    Closed Accounts Posts: 761 ✭✭✭PrecariousNuts


    No change in j direction
    Momentum before = momentum after etc
    relative velocity after = e (relative velocity before)

    It sounds right


  • #34
    DS
    Registered Users, Registered Users 2 Posts: 654 ✭✭✭DS


    Taking the line joining the centres of the spheres as the i direction:
    Momentum is conserved in the i direction.
    The j velocities of each sphere remain unchanged.
    e = (relative velocity in i direction after/relative velocity in i direction before)

    Nice mock alright. But on question 4 he got the weights mixed up in the diagrams. Not as accurate a bastard as I imagined :)


  • #35
    subway_ie
    Closed Accounts Posts: 1,122 ✭✭✭subway_ie


    Originally posted by Mutant_Fruit
    what are the laws governing the oblique collision of two spheres?

    When it says to "state the laws governing the oblique collision of two spheres" you've got to actually give the full explanation, ie:

    For two bodies impinging directly, their relative veloicty after impact is equal to a constant (e) times their relative velocity before impact and in the opposite direction.

    In any system of colliding coliding bodies, the total momentum of the bodies before interaction is equal to the total momentum after the interaction, provided no external force acts on the system.

    If you just give the equations, you'll get attempt marks at most.


  • #36
    subway_ie
    Closed Accounts Posts: 1,122 ✭✭✭subway_ie


    Originally posted by Mutant_Fruit
    EDIT: i did it three times...
    EDIT2: His solution is wrong! HAH, i'm not stupid after all. He thinks the wind is coming from the north east!, but its actually coming from south-east (i.e. going north WEST) Therefore he should have set (a-1) = MINUS(b+2) i believe.

    My solution is right.

    He seems to have gotten alot of solutions messed up - either small mistakes, or answering a totally different questions. It looks like it was all a bit of a rush job tbh.


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  • #37
    Mutant_Fruit
    Closed Accounts Posts: 4,943 ✭✭✭Mutant_Fruit


    makes you feel so smart when you realise you're better than some chap on the internet. :p


  • #38
    subway_ie
    Closed Accounts Posts: 1,122 ✭✭✭subway_ie


    Originally posted by Mutant_Fruit
    makes you feel so smart when you realise you're better than some chap on the internet. :p

    It's even better when you realise that he wrote your applied maths book and is supposed to be a complete genius...


  • #39
    Mutant_Fruit
    Closed Accounts Posts: 4,943 ✭✭✭Mutant_Fruit


    WTF?!?! Are you serious!

    Oh my god, i retract that statement before someone here posts it to him. :p

    i'm smarter

    EDIT: an answer for 10b would be nice, and that completes my Applied maths revision. 4 papers completed in 2 days, and i'll do some more thinking tomorrow :D


  • #40
    penguincakes
    Closed Accounts Posts: 124 ✭✭penguincakes


    Originally posted by subway_ie
    It's even better when you realise that he wrote your applied maths book and is supposed to be a complete genius...
    Oh he is. He was my teacher.


  • #41
    subway_ie
    Closed Accounts Posts: 1,122 ✭✭✭subway_ie


    Originally posted by Mutant_Fruit
    WTF?!?! Are you serious!

    Well, only if you're usin' that ancient brown one, "Fundamental Applied Mathematics" - you know, the one that *everybody* seems to misread as "Foundation Mathematics".

    I couldn't get 10 (b) to work out properly... I wonder if he just couldn't do it so he made a "mistake" and did a totally unrelated question in his solutions?


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  • #42
    Mutant_Fruit
    Closed Accounts Posts: 4,943 ✭✭✭Mutant_Fruit


    thats what i was thinking :p

    I got a really wierd answer, but i couldn't care less really. Its never going to be that messy in a LC exam, even part A was extremely messy. fourth roots! Feck off is what i say.
    i still got it right though :p


  • #43
    DS
    Registered Users, Registered Users 2 Posts: 654 ✭✭✭DS


    I got 10b out. I think part (iii) has to be a misprint. It should read o instead of a, because the nucelus starts from a, so it is nearest to a when it's at a, so question makes no sense. I'm only noticing this now as I'm typing the solution. I actually misread the question the correct way. What are the feckin chances of that jesus christ. Anyway it works out perfectly assuming (iii) reads distance from o when closest to o.

    (i)
    F=ma
    F=mk^2x^-5
    a=k^2x^-5
    a=vdv/dx=k^2x^-5
    vdv=k^2x^-5dx

    (ii)
    1/2(v^2)=-1/4(k^2x^-4)
    2v^2=-k^2x^-4 + c
    v=2kroot(3)/d^2 when x=d (that caught me out at first, put x=0, but if you read the question carefully x=d at t=0)
    works out to c=25k^2/d^4
    2v^2 = 25k^2/d^4 - k^2x^-4
    get v at midpoint i.e. x = d/2
    2v^2=9k^2/d^4
    v=3k/(root(2)d^2)

    (iii)
    condition is v=0
    2v^2 = 25k^2/d^4 - k^2x^-4
    25k^2/d^4 - k^2x^-4 = 0
    25k^2/d^4 = k^2x^-4
    solve for x -> x=d/root(5)

    Does seem a very rushed job, I didn't recognise some of the solutions as Q's on the paper.


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