Sleeping well due to physics
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 .
- You may neglect the weight of the top of the mattress.
The answer is 98000.
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1 solution
If I am lying down comfortably I have come to equilibrium. Therefore there is no net force on me as I rest and the spring force of the mattress must compensate for the gravitational force. We then have k Δ y = m g which yields a value of 9 8 , 0 0 0 for the spring constant k .