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Mechanics - Centre of Mass Question - Help?

A stone sculpture consists of a 2m (length) x 1.6m (height) x 1m (width), cuboid surmounted by a cylinder of radius x metres and length 1 m .

The centre of mass of the sculpture is a point of contact between the two parts. Find x.

.... I have some idea of what to do, but I need some help with it :smile:
Reply 1
You will know where the heights of the 2 CoM are

To find the height of the overall CoM you would do (V1h1 + V2h2)/(V1+V2) ... since you know this height and you know everything apart from V2 you can find V2 and therefore the radius

(I am assuming that both parts are made from the same material so that Volume is proportional to mass)
Reply 2
Original post by TenOfThem
You will know where the heights of the 2 CoM are

To find the height of the overall CoM you would do (V1h1 + V2h2)/(V1+V2) ... since you know this height and you know everything apart from V2 you can find V2 and therefore the radius

(I am assuming that both parts are made from the same material so that Volume is proportional to mass)


so, as the height of the CoM is 1.6m (where they touch) =>

1.6 = (V1h1 + V2h2)/(V1+V2)

V1 = 3.2
h1 = 0.8
v2 = pi x^2
h2 = (1.6 + x)

1.6 = ((3.2*0.8) + ((pi x^2 * (1.6 + x) )) / (3.2 + pi x^2)

----

Have I got that right? I doesn't seam to give an answer for x which seams right...
Reply 3
Original post by Logan234
so, as the height of the CoM is 1.6m (where they touch) =>

1.6 = (V1h1 + V2h2)/(V1+V2)

V1 = 3.2
h1 = 0.8
v2 = pi x^2
h2 = (1.6 + x)

1.6 = ((3.2*0.8) + ((pi x^2 * (1.6 + x) )) / (3.2 + pi x^2)

----

Have I got that right? I doesn't seam to give an answer for x which seams right...



Did you have a picture
Which way round is the cylinder ... I assumed that it was stood on a circular face so that h2 would = 1.6+0.5
Reply 4
Original post by TenOfThem
Did you have a picture
Which way round is the cylinder ... I assumed that it was stood on a circular face so that h2 would = 1.6+0.5


Reply 5
Original post by TenOfThem
Did you have a picture
Which way round is the cylinder ... I assumed that it was stood on a circular face so that h2 would = 1.6+0.5


It not very helpful, but this is the copy of the image it gave :/

http://www.tiikoni.com/tis/view/image.php?id=82e98c9
Reply 6
Original post by Logan234


o_0 weird picture issue xD,
Reply 7
V1 = 3.2
h1 = 0.8
v2 = pi x^2
h2 = (1.6 + x)

1.6 = ((3.2*0.8) + ((pi x^2 * (1.6 + x) )) / (3.2 + pi x^2)

So, as you say

[br]1.6=(2.56+1.6pix2+pix3)/(3.2+pix2)[br][br]1.6 = (2.56 + 1.6pix^2 +pix^3)/(3.2 + pix^2)[br]
(edited 12 years ago)
Reply 8
So
[br]5.12+1.6pix2=2.56+1.6pix2+pix3[br][br]5.12 + 1.6pix^2 = 2.56 + 1.6pix^2 + pix^3[br]

Giving quite a simple answer
(edited 12 years ago)
Reply 9
Original post by TenOfThem
So
[br]5.12+1.6pix2=2.56+1.6pix2+pix3[br][br]5.12 + 1.6pix^2 = 2.56 + 1.6pix^2 + pix^3[br]

Giving quite a simple answer


yes, this is what I got, giving, x = -0.452 , 0.521 , 3.45 .... which of these is correct though? Im guessing its not the negative value...
Original post by Logan234
yes, this is what I got, giving, x = -0.452 , 0.521 , 3.45 .... which of these is correct though? Im guessing its not the negative value...


it only gives one answer

x = 0.934

How did you get the answers you have
Reply 11
Original post by TenOfThem
it only gives one answer

x = 0.934

How did you get the answers you have


actually, your answer is correct there, I typed it wrong into my calculator :smile:

yeh, wow, that's done then, x= 0.934 , THANK YOU SO MUCH! <3 XD
np

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