M2 centre of mass

Need some help with 3ii.
What am I doing wrong?

Have you attached working?

It's possible I can't see anything due to my workplace's firewall (as imgur and other sites are blocked) but it's necessary to provide working in order for helpers to tell you where you went wrong!

Need some help with 3ii.
What am I doing wrong?

Mass of rectangle = 16,000
Mass of semi circle = 800pi

You've assumed that the area is proportional to the mass. This is true for a uniform lamina, but considering the door as a whole, the semicircle and rectangle are not necessarily of the same density, even though each is uniform in itself.

You need to use the weights rather than the areas.

I see. I'm a bit rusty with moments do you mind helping with 3i?

I tried taking moments about each point but I don't think I am doing it right.

M(G) = 40 * 60 = 140 * X

You've missed the weight of the semicircular section. Else, looks fine.

Cheers

Last one if you don't mind.

If I am taking moments about A do I need to know the distance of the dotted line?

Cheers

Last one if you don't mind.

If I am taking moments about A do I need to know the distance of the dotted line?

From A, yes, you do.

Note: The distance of the centre of mass of a uniform triangular lamina is 1/3 the perpendicular height from any side

hmm how would I take moments about A

12 * Tsin30 = 8 * 3 * 2g?

Where's the "3" come from?

Isn't that the distance of the dotted line?

For moments, you want the perpendicular distance of the line of action of the force.

In this case, that distance from A is 8. The 3 doesn't come into it.