worlds fair ornament

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An ornament for a courtyard at a World's Fair is to be made up of four identical, frictionless metal spheres, each weighing 2√6 ton-wts . The spheres are to be arranged as shown, with three resting on a horizontal surface and touching each other; the fourth is to rest freely on the other three. The bottom three are kept from separating by spot welds at the points of contact with each other. Allowing for a factor of 3, how much tension must the spot welds withstand?

Answer


Solutions (listed by author)

Michael A. Gottlieb (using forces) (pdf, 188K)  [Much thanks to Doug Krajnovich and Samuel Hornus for their comments and corrections. mg]

Michael A. Gottlieb (using virtual work) (pdf, 70K)  [Geoff Wright gave me this  idea. mg]

 

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