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M1 show that question (forces)

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    I am stuck on the show that part (b)

    A string is threaded through a smooth ring of weight W and is tied to two points A and B on the same level. The ring is pulled by a horizontal force, P, so that the two parts of the string are inclined at angles of 60 deg and 30 deg respectively to the vertical.

    a) draw the two possible configurations which fit the given facts.

    This part I understand and the attached graphics are the two configurations.

    The next part is bit I am stuck on:

    b) Show that in each case the tension in the string is W(root(3) - 1).

    Here is my working.

    Vertically

    Tsin60 + Tsin30 = W

    T(\frac{\sqrt{3}}{2} + \frac{1}{2}) = W

    T = \frac{2W}{\sqrt{3} + 1}

    So how do I get W(\sqrt{3} - 1)
    Attached Thumbnails
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    (Original post by acomber)
    ...
    Rationalize the denominator; multiply top and bottom by (think about it first before looking):


    Spoiler:
    Show

    1-\sqrt{3} or \sqrt{3}-1
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    (Original post by ghostwalker)
    Rationalize the denominator; multiply top and bottom by (think about it first before looking):


    Spoiler:
    Show

    1-\sqrt{3} or \sqrt{3}-1
    Wow. Thanks for tip - didn't need spoiler - more satisfying working out myself.
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    (Original post by acomber)
    Wow. Thanks for tip - didn't need spoiler - more satisfying working out myself.
    :cool:

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