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M2 Framework Edexcel question

Hi, I'm using the Edexcel Heinmemann M2 book and i'm stuck on ex 2E question 7. I'd really appreciate some help :smile:

"ACB is a semicircle of radius 3cm, centre O. ADO and BEO are both semi circles of radius 1.5cm. Find the position of the centre of mass of the framework."

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Using l=rθ and rsina/a= distance from centre of circle of an arc
{1.5pi [1.5sin(pi/2)/pi/2] }2 + 3pi[3sin(pi/2)/pi/2] = 6pi (ybar)

9+18 = 6pi (ybar)

27=6pi (ybar)

9/2pi when the answer in the back of the book is 3/2pi from AB


I've tried the solution bank and my computer doesn't let me see the answer to question 7, yet I tried all the others and they worked perfectly fine...
Original post by Mrs Huntley
...


The two small semicircles are on the opposite side of AB to the large semicircle, so one of those sets will have a negative y co-ordinate, depending on which direction you take as positive.
Reply 2
Original post by ghostwalker
The two small semicircles are on the opposite side of AB to the large semicircle, so one of those sets will have a negative y co-ordinate, depending on which direction you take as positive.


I did that in my first attempt (now on something stupid like my 5th attempt) and they cancel out to 0 in the end
Original post by Mrs Huntley
I did that in my first attempt (now on something stupid like my 5th attempt) and they cancel out to 0 in the end


Shouldn't do. You just need to flip the sign in the middle of

"{1.5pi [1.5sin(pi/2)/pi/2] }2 + 3pi[3sin(pi/2)/pi/2] = 6pi (ybar)"

and similarly the rest of your working as appropriate.
Reply 4
I'm still somewhat confused, when I swap the sign of semicircle ADO so that its radius is -1.5 I get the same answer as before :s-smilie:

When you said
Original post by ghostwalker
Shouldn't do. You just need to flip the sign in the middle of

"{1.5pi [1.5sin(pi/2)/pi/2] }2 + 3pi[3sin(pi/2)/pi/2] = 6pi (ybar)"

and similarly the rest of your working as appropriate.


why do I need to minus 3 pi?
Original post by Mrs Huntley
I'm still somewhat confused, when I swap the sign of semicircle ADO so that its radius is -1.5 I get the same answer as before :s-smilie:

When you said

why do I need to minus 3 pi?


Since you're taking distances of centres of gravity relative to the line AB, you're using that as the zero in the y direction.

The two smaller semicircles are above the line hence their CofG is positive, and the larger semicircle is below the line, and hence its CofG is negative.

You don't need to flip the sign of semicirlce circle ADO. Don't forget you're working in the y direction, not the x direction.
(edited 11 years ago)
Reply 6
Original post by ghostwalker
Since you're taking distances of centres of gravity relative to the line AB, you're using that as the zero in the y direction.

The two smaller semicircles are above the line hence there CofG is positive, and the larger semicircle is below the line, and hence its CofG is negative.


THANK YOU SO MUCH! :grin: I finally understand!
Original post by Mrs Huntley
THANK YOU SO MUCH! :grin: I finally understand!


:cool:

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