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# Centre of gravity

1. Find the centre of gravity of a piece of wire 14cm long, bent into an L-shape with the upright part 8cm long. (With steps please. Urgent!!!)

Update:

Can you please also explain why the mass ratio of two sections is 3:4? Thanks a lot!

Update 2:

Sorry!!! My meaning is if the mass ratio of two sections is 3:4, then why

x: (5-x) is also 3:4? Thanks a lot!!!

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Suppose that the wire is uniform in thickness, we have the shape like:

With points A and B being the centres of gravity of respective sections of wire, they are 4 cm and 3 cm from the point of joining respectively.

Then we draw a line along AB and the centre of gravity of the whole shape will be on a point of the line.

The sections have their mass ratio 3:4 and so, supposing that the centre of gravity of the shape is x cm from B, we have:

3x = 4(5 - x)

x = 20/7 cm

2009-02-26 22:55:49 補充：

This is related to the problem of taking moment (turning force):

Suppose that mass 3m is placed at point B and mass 4m is placed at point A, then when the moment is taken about the centre of gravity, we have:

Moment contributed by the mass 3m = (3m)x

Moment contributed by the mass 4m = (4m)(5 - x)

2009-02-26 22:56:01 補充：

So 3x = 4(5 - x)

For more details in turning force, pls. visit:

http://en.wikipedia.org/wiki/Torque

Source(s): My physics knowledge