Sleeping well due to physics

Classical Mechanics Level 2

Everybody has their own preference for hard or soft mattresses. Personally, I don't like to sleep on a mattress that sinks more than 1 cm after I lie down on it and come to rest. If we model a mattress as a big spring, what is the minimum spring constant in N/m of the mattress so that I, at a mass of 100 kg, don't sink more than 1 cm into the mattress when I lie down?

Details and assumptions

  • The acceleration due to gravity is \(-9.8~\mbox{m/s}^2\).
  • You may neglect the weight of the top of the mattress.

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