Mechanics Problem from MEXT scholarship 2007

[rwssman]

<Moderator's note: User has been warned to show some effort.>

1. Homework Statement

Here this is a problem that I get troubled from MEXT scholarship examination.

And the problem is

Homework Equations

F = mg
Fx = cosa
Fy = sina

The Attempt at a Solution

Is anyone can help me to solve the problem. I read but I don't know what to start. Thank you.

 

[haruspex]

Homework Statement

Here this is a problem that I get troubled from MEXT scholarship examination.
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View attachment 240316

And the problem is
View attachment 240319
View attachment 240318

Homework Equations

F = mg
Fx = cosa
Fy = sina

The Attempt at a Solution

Is anyone can help me to solve the problem. I read but I don't know what to start. Thank you.

First thing is to check whether the diagram looks reasonable. What should be the relationships between the positions of A, B, D, E and G?

 

[rwssman]

Now, I don't know how to find that relationship rather than mathematics.

 

[haruspex]

Now, I don't know how to find that relationship rather than mathematics.

First, what is the relationship between A, G and E?
Next, what do the lines AD, BD and DG represent? Why are they shown meeting at a point (D)?
What is the angle ABD? (Very different from what it looks in the diagram.)

 

[rwssman]

A, G and E is in the same line.
AD, BD, and DG represent force perpendicular to the hemisphere.
I don't know the next.

 

[haruspex]

A, G and E is in the same line.

There's more to it than that. What does point G represent?

AD, BD, and DG represent force perpendicular to the hemisphere.

AD and BD represent normal forces, and yes, AD is perpendicular to the hemisphere, but what should BD's direction be?
Given the meaning of G, what force does DG represent?
Why must these three forces pass through a single point?

 

[rwssman]

OK, Now I drew a diagram and solve problem number 1 and 2 already, I know that a is pi/2 and b is theta. But in problems number 3,4, and 5 I still don't know whether it is possible or impossible.

 

[haruspex]

OK, Now I drew a diagram and solve problem number 1 and 2 already, I know that a is pi/2 and b is theta. But in problems number 3,4, and 5 I still don't know whether it is possible or impossible.

3 can be answered very easily, but might as well proceed straight to the general case.
Write out the usual horizontal and vertical force balance equations, and a moments equation for some suitable axis.