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!!!)
Can you please also explain why the mass ratio of two sections is 3:4? Thanks a lot!
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!!!
- 魏王將張遼Lv 71 decade agoFavorite Answer
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:Source(s): My physics knowledge