Tension for the crown

The blacksmiths of the kingdom of Mechania are wondering how much tension is holding a crown together as it rests on the head of their sovereign. The king of Mechania has a frictionless, perfectly spherical head with radius r=10 cmr = 10 \text{ cm}, and the crown is a thin cord with a length of =37.7 cm \ell = 37.7 \text{ cm} and a mass of m=628.32 g.m = 628.32 \text{ g}.

Compute the tension in the crown (in Newtons).

Assumptions:

  • The crown has no thickness and rests perfectly level (that is, it makes a circle which is contained in a plane parallel to the horizontal).
  • The gravitational constant of Mechania is g=10 m/s2.g = 10 \text{ m/s}^2.
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