Pyramid of Spheres physics question plz help

Three identical spheres of mass m and radius a are in a triangular arrangement on a horizontal plane, spot welded together where they touch. Another sphere is placed on top of the first three, with the same density but a different radius ka. Assume where necessary that the contacts are smooth.

What is the tension in the weld necessary to keep the pyramid stable?

I have barely any idea how to work this out can anyone plz point me in the right direction

Reply 1

mqb2766

Original post

by akashDTV

Three identical spheres of mass m and radius a are in a triangular arrangement on a horizontal plane, spot welded together where they touch. Another sphere is placed on top of the first three, with the same density but a different radius ka. Assume where necessary that the contacts are smooth.
What is the tension in the weld necessary to keep the pyramid stable?
I have barely any idea how to work this out can anyone plz point me in the right direction

You could consider a 2d case with two circles on the base (single weld) and a third one on top. Then the usual horizontal and vertical forces and moments.

The 3d case builds on this and is covered in the hints?

Reply 2

Eimmanuel

Study Forum Helper

Original post

by akashDTV

This problem seems to be an extension of this problem.
https://isaacphysics.org/questions/three_spheres

You can attempt this problem first to have a feel of what is happening.
Then apply your understanding to the problem that you want to solve.

This problem has more hints and you need to understand them. :smile: