C2 Help pleeeeease

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  1. MikeySwansea's Avatar
    1 17-05-2012  23:21
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    C2 Help pleeeeease
    L = Rθ - rθ

    K = .5(R^2θ - r^2θ)

    Find an expression for r in terms of R, K and L

    I manipulated the first equation to get:
    r = R - L/θ

    and the 2nd one to get:
    r^2 = R^2 - 2K/θ

    I then divided the second equation by the first one to get:
    r = R - 2K/L


    However, the mark scheme says the answer is r = 2K/L - R

    Would really appreciate it if someone could explain to me why my method is wrong. Got C2 at 9am!
  2. peachesandcream77's Avatar
    2 17-05-2012  23:27
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    • Posts: 321
    Re: C2 Help pleeeeease
    are you doing OCR?
  3. MikeySwansea's Avatar
    3 17-05-2012  23:29
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    • Posts: 323
    Re: C2 Help pleeeeease
    (Original post by peachesandcream77)
    are you doing OCR?
    Nope, WJEC
  4. Intriguing Alias's Avatar
    4 17-05-2012  23:43
    • TSR Idol
    • Location: Yorkshire
    Re: C2 Help pleeeeease
    (Original post by MikeySwansea)
    L = Rθ - rθ

    K = .5(R^2θ - r^2θ)

    Find an expression for r in terms of R, K and L

    I manipulated the first equation to get:
    r = R - L/θ

    and the 2nd one to get:
    r^2 = R^2 - 2K/θ

    I then divided the second equation by the first one to get:
    r = R - 2K/L


    However, the mark scheme says the answer is r = 2K/L - R

    Would really appreciate it if someone could explain to me why my method is wrong. Got C2 at 9am!
    you're doing \dfrac{R^2 - 2K/\theta}{R-2K/L}

    What makes you think that = R - 2K/L

    You can't just divide one part by the part below it.

    that's like saying \dfrac{x+3}{y-7} = \frac{x}{y} - \frac{3}{7} which obviously is not true.
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    1
  5. raheem94's Avatar
    5 17-05-2012  23:52
    • TSR Demigod
    • Posts: 5,512
    Re: C2 Help pleeeeease
    (Original post by MikeySwansea)
    L = Rθ - rθ

    K = .5(R^2θ - r^2θ)

    Find an expression for r in terms of R, K and L

    I manipulated the first equation to get:
    r = R - L/θ

    and the 2nd one to get:
    r^2 = R^2 - 2K/θ

    I then divided the second equation by the first one to get:
    r = R - 2K/L


    However, the mark scheme says the answer is r = 2K/L - R

    Would really appreciate it if someone could explain to me why my method is wrong. Got C2 at 9am!
    \displaystyle L = R \theta - r \theta \implies L = \theta (R-r) \longrightarrow (1) \\ k = \frac12 (R^2 \theta - r^2 \theta ) \implies 2k = \theta (R^2 - r^2) \implies 2k = \theta (R-r)(R+r) \longrightarrow (2)

    Now divide equation (2) \ \ by \ \ (1)

    \displaystyle \frac{2k}{L} = \frac{ \theta (R-r)(R+r)}{\theta (R-r)} \implies \frac{2K}{L} = R + r \implies 2k = RL + rL \\ \implies rL = 2k - RL \implies r = \frac{2k-RL}{L} \implies \boxed{ r = \frac{2k}{L} - R }

    I gave a full solution because the OP's exam is tomorrow.
    Post rating:
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  6. MikeySwansea's Avatar
    6 17-05-2012  23:54
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    • Posts: 323
    Re: C2 Help pleeeeease
    (Original post by hassi94)
    you're doing \dfrac{R^2 - 2K/\theta}{R-2K/L}

    What makes you think that = R - 2K/L

    You can't just divide one part by the part below it.

    that's like saying \dfrac{x+3}{y-7} = \frac{x}{y} - \frac{3}{7} which obviously is not true.
    Thank you Hassi

    Edit: you to Raheem
    Last edited by MikeySwansea; 17-05-2012 at 23:57.
  7. Intriguing Alias's Avatar
    7 17-05-2012  23:56
    • TSR Idol
    • Location: Yorkshire
    Re: C2 Help pleeeeease
    (Original post by raheem94)
    \displaystyle L = R \theta - r \theta \implies L = \theta (R-r) \longrightarrow (1) \\ k = \frac12 (R^2 \theta - r^2 \theta ) \implies 2k = \theta (R^2 - r^2) \implies 2k = \theta (R-r)(R+r) \longrightarrow (2)

    Now divide equation (2) \ \ by \ \ (1)

    \displaystyle \frac{2k}{L} = \frac{ \theta (R-r)(R+r)}{\theta (R-r)} \implies \frac{2K}{L} = R + r \implies 2k = RL + rL \\ \implies rL = 2k - RL \implies r = \frac{2k-RL}{L} \implies \boxed{ r = \frac{2k}{L} - R }

    I gave a full solution because the OP's exam is tomorrow.
    P.S The last 3-4 steps are redundant. You multiplied by L and then divided by L.
  8. raheem94's Avatar
    8 18-05-2012  00:02
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    Re: C2 Help pleeeeease
    (Original post by hassi94)
    P.S The last 3-4 steps are redundant. You multiplied by L and then divided by L.
    I was being foolish. :mad:

    I have an S1 exam tomorrow, so i was revising for it, didn't noticed what i am writing.
  9. Intriguing Alias's Avatar
    9 18-05-2012  00:05
    • TSR Idol
    • Location: Yorkshire
    Re: C2 Help pleeeeease
    (Original post by raheem94)
    I was being foolish. :mad:

    I have an S1 exam tomorrow, so i was revising for it, didn't noticed what i am writing.
    Aha it's no problem I just thought I'd let you know. Good luck with S1 I'm sure you'll nail it mate
  10. raheem94's Avatar
    10 18-05-2012  00:11
    • TSR Demigod
    • Posts: 5,512
    Re: C2 Help pleeeeease
    (Original post by hassi94)
    Aha it's no problem I just thought I'd let you know. Good luck with S1 I'm sure you'll nail it mate
    Hoping for a simple probability question, other chapters are fine.

    When is your first exam?
  11. Intriguing Alias's Avatar
    11 18-05-2012  00:15
    • TSR Idol
    • Location: Yorkshire
    Re: C2 Help pleeeeease
    (Original post by raheem94)
    Hoping for a simple probability question, other chapters are fine.

    When is your first exam?
    A month today so quite a while away (Physics Unit 5).
  12. raheem94's Avatar
    12 18-05-2012  00:22
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    • Posts: 5,512
    Re: C2 Help pleeeeease
    (Original post by hassi94)
    A month today so quite a while away (Physics Unit 5).
    Physics with which board?
    You would be looking forward for an A* in physics, right? How many marks do you need for it?
  13. Intriguing Alias's Avatar
    13 18-05-2012  00:26
    • TSR Idol
    • Location: Yorkshire
    Re: C2 Help pleeeeease
    (Original post by raheem94)
    Physics with which board?
    You would be looking forward for an A* in physics, right? How many marks do you need for it?
    AQA. I'd hope so but I didn't do great in January so it will be very hard. I need about 112-114/120 (depending on what my ISA mark scales to UMS-wise). While I could probably do this given enough effort - I don't want to put in the effort if it means compromising a STEP grade.
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