March 28, 2017

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An air mattress is 2.1 m long, 0.55 m wide, and 13 cm deep. If the air mattress itself has a mass of 0.22 kg, what is the maximum mass it can support in fresh water?
I know that I can find the volume and area, and the density of water. But I cannot find an equation to find the max weight that can be added to the matress. Can someone help?

The maximum mass it can support without sinking (Mmax), PLUS its own mass, equals the mass of the water displaced. The mattress' volume is
V = 2.1x0.55x0.13 = 0.1502 m^3.
(10^3 kg/m^3) V = Mmax + 0.22 kg
Mmax = 150.2 kg - 0.22 kg = 150.0 kg.

The mass of the air mattress does not make a lot of difference in the answer in this case.

Thank you so much!!! It was correct.

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