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M2 centres of mass (solved) - good practice watch

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    a template for the cross section of a tunnel for a model railway consists of a uniform rectangular sheet of metal ABCD, where AB=6cm and BC=3cm, from which a semicircle of radius 2cm and centre X, where X is the mid-point of CD, has been but away.

    a) find the distance of the centre of mass of the template from CD, giving your answer in cm to 2 dp

    the template is stored by hanging it on a small rough peg which touches the template at a point P on the semi-circular section of the perimeter. given that the template hangs in a vertical plane with edges AD and BC horizontal,

    b) find, to the nearest degree, the acute angle that PX makes with the vertical

    c) explain why the template can rest in such position only if the contact between the peg and the template is rough.

    ---------

    part A is okay, i found that the distance is 3.01cm...

    but then... ive no idea where to start for question b....

    anyone got ideas??


    thxxx
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    Two facts are important to determine where P is.

    1) DA and BC are horizontal.

    2) The centre of gravity of a freely hanging object is always vertically below the point of suspension.

    Drawing a diagram would be useful here.
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    but if that was the case, i must have done part A wrong... coz my answer for part A was 3.01 cm... (since the radius of the semicircle is 2....)
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    (Original post by seniocs)
    but if that was the case, i must have done part A wrong... coz my answer for part A was 3.01 cm... (since the radius of the semicircle is 2....)
    Indeed. Since the lamina is only 3 cm from CD to AB, I think you've made an error there.

    I'm signing off for a bit, as I need to cook and eat!
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    problem solved... thx mate
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    is the answer for A) 1.85?
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    (Original post by hhfgefgew)
    is the answer for A) 1.85?
    Yes.
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    okay im stuck on the same question - ive managed part a but i cant even work out the diagram for part b in the slightest as i cant see how you can have BC and AD horizont
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    (Original post by penta)
    okay im stuck on the same question - ive managed part a but i cant even work out the diagram for part b in the slightest as i cant see how you can have BC and AD horizont
    Don't forget the peg is rough so the template isn't going to slide if the edge at the point of suspension isn't horizontal.

    On your initial diagram, mark on the centre of mass with reasonable accuracy.

    If BC,AD are horizontal, then AB,CD must be vertical. You also know that the centre of mass must be vertically below the peg.

    Rotate your diagram 90 degrees if it helps.

    Can you see where the peg must touch the template now?
 
 
 
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Updated: August 24, 2014
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