- #1

gnits

- 137

- 46

- Homework Statement
- To find the center of gravity of a quadrilateral

- Relevant Equations
- Moments

Could I please ask for help with the following question. Part 2 is my problem. I have no idea how to begin, any hints would be much appreciated:

I'm ok here, done that.

Here is a diagram:

(The blue and orange strokes are meant to show the equality of the lengths of the segments that they are on)

I don't mind which way it is proved, by equivalent particle systems or "otherwise".

I started by setting up cartesian coordinates at A, but I don't think that helps.

Thanks for any help,

Mitch,

*1) Prove that the center of gravity of a uniform triangular lamina is the same as that of three equal particles placed at the vertices of the lamina*I'm ok here, done that.

*2) A uniform lamina of weight W is in the shape of a quadrilateral ABCD. The diagonals AC, BC meet at P, where AP < PC, BP < PD and Q, R are points on AC, BD respectively such that QC = AP, RD = BP. By replacing the triangles ABD, BCD by equivalent systems of particles, or otherwise, prove that the center of gravity of the lamina is the same as that of a particle of weight W/3 at Q and a particle of weight 2W/3 at the midpoint of BD.*Here is a diagram:

(The blue and orange strokes are meant to show the equality of the lengths of the segments that they are on)

I don't mind which way it is proved, by equivalent particle systems or "otherwise".

I started by setting up cartesian coordinates at A, but I don't think that helps.

Thanks for any help,

Mitch,