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, 69K)

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

 

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