Question

A uniform rectangular parallelepiped of sides l, 2l, and 4l lies on a horizontal plane on each of its three different faces, in turn. What is the potential energy of the parallelepiped in each of these positions? In which of these positions is it the most stable. 

Answer 1

The potential energy E_n of the parallelepiped in the different positions will be.: 

E₁ = 2 mgl when it lies on its smallest face; 

E₂ = mgl when it lies on its next largest face; 

E₃= 1/2 mgl when it lies on its largest face.

The most stable position, corresponding to the minimum value of the potential energy of the body, will be in the last of the above three cases.