Maximum tilting angle of a composite body

[unknown_2]

Homework Statement

What is the maximum angle you can rotate the cone before the scoop falls out? Assume that the scoop of ice cream acts like a perfect sphere and does not stick to the cone.

calculated already that the center of mass is located at z = 5.02

Assume that the scoop of ice cream is a sphere with radius r = 1.51in and is placed into a 4.00 in tall cone. The interior height of the cone is 3.60 in. The exterior radius of the cone is 1.25 in and the interior radius is 1.10 in.

Homework Equations

$$\theta$$ = atan (x/z) [i got this from the answers section of a similar problem]

where:
-x is something i don't know
-z is the center of mass in the z direction

The Attempt at a Solution

no clue where to start.
i looked at similar problem but they weren't much help. i don't really understand the concept of how this works.

any help would b nice

cheers,

 

[Asteroid1]

When do you think the ball will fall from the cone? Try it out with a glass and a ball.

You will see that once the center of mass of the ball goes 'further' than the point it is resting on, it will fall out.

Now you'll just have to figure out at what angle that will be.

 

[unknown_2]

sry for the late reply, just got my internet fixed. so i understand what u said. so from my figure:

r = 1.51
x = 1.10

so i solved for $$\phi$$ :

$$\phi$$ = 180 - ($$cos^{-1}$$$$\frac{1.10}{1.51}$$ + 90)
= $$46.75^{o}$$

so then the sum of all the angles in the larger triangle will be 180 so:
$$\theta$$ = 180 - ($$\phi$$+90)
=$$43.24^{o}$$

since it's simmilar triangles so the tilting angle is $$43.24^{o}$$?

 

[unknown_2]

can any1 shed some light on what i did wrong.