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Math Help - trapezoid

  1. #1
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    trapezoid

    Hi, I need some help on this question.

    A unifom lamina ABCEF is obtained from a rectangle ABCD with AB = CD = 8cm and BC = AD = 6cm, by removing the triangle EDF, where E and F lie on CD, AD respectively, with CE = 2cm and AF = 3cm.

    1. Find the distance of the centre of mass of the lamina ABCEF from AB and AD.

    2. The lamina is suspended freely from F and hangs in equilibrium under gravity. Find the angle which AF makes with the vertical.

    I'm stuck and don't know how to start.
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  2. #2
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    It's a rectangle with uniform density.

    I would situate it on a set of coordinate axes, with A at the Origin and B on the Positive x-axis. This puts D on the Positive y-axis.

    Area of FDE = ??
    Area of AFECB = ??

    Center of Mass of FDE = (??,??)
    Center of Mass of AFECB = (??,??)

    Fill in the blanks and let's see where that leads us?
    Last edited by TKHunny; November 28th 2007 at 07:48 AM. Reason: Revised to make sense and to conform to CaptainBlack's Diagram.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by novadragon849 View Post
    Hi, I need some help on this question.

    A unifom lamina ABCEF is obtained from a rectangle ABCD with AB = CD = 8cm and BC = AD = 6cm, by removing the triangle EDF, where E and F lie on CD, AD respectively, with CE = 2cm and AF = 3cm.

    1. Find the distance of the centre of mass of the lamina ABCEF from AB and AD.

    2. The lamina is suspended freely from F and hangs in equilibrium under gravity. Find the angle which AF makes with the vertical.

    I'm stuck and don't know how to start.
    You start by drawing a diagram.

    RonL
    Attached Thumbnails Attached Thumbnails trapezoid-gash.jpg  
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  4. #4
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    Hi, guys Im still stuck on this question cause I got answer's that is completely wrong like distance from AB as 6 and AD as 2 so can anyone show me a step to step cause im hopeless on this.
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  5. #5
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    Use the very clear drawing and fill in the blanks I suggested.

    Let's see what you get.
    Last edited by TKHunny; November 28th 2007 at 01:35 PM.
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  6. #6
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    Quote Originally Posted by novadragon849 View Post
    Hi, I need some help on this question.

    A unifom lamina ABCEF is obtained from a rectangle ABCD with AB = CD = 8cm and BC = AD = 6cm, by removing the triangle EDF, where E and F lie on CD, AD respectively, with CE = 2cm and AF = 3cm.

    1. Find the distance of the centre of mass of the lamina ABCEF from AB and AD.

    2. The lamina is suspended freely from F and hangs in equilibrium under gravity. Find the angle which AF makes with the vertical.

    I'm stuck and don't know how to start.
    Hello,

    to #1:

    I take the drawing of CaptainBlack.

    The area of the pentagon ABCEF can be calculated by Area of rectangle - area of right triangle = 6 \cdot 8 - \frac12 \cdot 6 \cdot 3 = 39

    Now choose 2 lines of equilibrum that means if you support the pentagon along the line the pentagon is in equilibrum. Thats only possible if the areas on both sides of such a line of equilibrum are equal.

    First I was looking for a right triangle with an area of 19.5 cm² (in red)

    Next I was looking for a trapezium with an area of 19.5 cm² (in blue)

    The intersection of these 2 lines is the centre of mass.

    As you see you get 2 congruent triangles thus the centre of mass is the midpoint of the lines of equilibrum.

    I'll leave the rest for you.
    Attached Thumbnails Attached Thumbnails trapezoid-schwerpkt_5eck.gif  
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by CaptainBlack View Post
    You start by drawing a diagram.

    RonL
    Note deliberate error in attachment AF should be 3cm not 2cm marked.
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  8. #8
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    Thanks finally got it right.
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