Resolving Forces for Composite Shape: Cone with Attached Ring | Mass: 52kg

[dennis1984]

Homework Statement

there is a composite shape (cone with ring attached at open end) total mass 52kg,cone m=22kg, ring=30kg find the 2 forces acting vertically upwards. the shape is lying on its side 21deg from the horizontal.

Homework Equations

(xtotal x mtotal) = (xcone x mcone) + (xring x mring)
balance forces ( up=down and left=right)

The Attempt at a Solution

find the CG using (xtotal x mtotal) = (xcone x mcone) + (xring x mring)
resolve forces into verical and horizontal components
balance forces
the problem I am having is that one force is acting through the centrline at the tip of the cone and the other force is acting at the bottom point of the ring ( see pic)

please help i am pulling my hair out!

 

[omoplata]

Also consider the torque. What should the total torque around any point be, if the object is at equilibrium? Then you have enough info to find the forces.

 

[Spinnor]

See my sketch, can you determine distances L_1 and L_2? If so take moments about points A and B and the problem is done?

 

[omoplata]

Yes, if you have distances L_1 and L_2, the forces can be found by considering the moments about A and B.

Distances L_1 and L_2 can be found using geometry. The pdf you attached in your original post has all the information needed.

 

[dennis1984]

thank you very much for your replies,


for equilibrium: clockwise moments must equal anti clockwise moments

and because the forces are not perpendicular or parallel to the centreline of the CG the distances L1 and L2 must be the perpendicular distances from the CG to the line of action of the forces.

i have to basically work out the forces at various angles until the cone is vertical to make sure the forces shown in the diagram do not exceed a certain limit as the object is rotated so the same concept of resolving the forces into components(because of the angle that the object is at) and then taking moments will apply.