A classical mechanics problem by Kelvin Hong

There is a unit tetrahedron \(ABCD\) with face \(BCD\) on the ground. Edge \(CD\) is fixed to the ground so that vertex \(B\) can be lifted up. Now, James wants to exert a force horizontally on point \(A\) and turn over the tetrahedron, making vertex \(B\) the new apex with face \(ACD\) on the ground.

If the mass of the tetrahedron is \(m\), and the minimum force that is necessary to pull it can be expressed as \(\frac{mg}{a\sqrt{b}}\), where \(b\) is a square-free number, then submit \(a+b\).

Details and Assumptions:

  • \(g\) is the gravitational acceleration.
  • A unit tetrahedron is a tetrahedron with all six sides of length 1.

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