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Answer on Mechanics | Relativity Question for Mike

Question #1397
A 4.9 kg rectangular air mattress is 2.7 m
long, 1.16 m wide, and 0.183 m thick.
What mass can it support in water before
sinking?
Answer in units of kg.
Expert's answer
The object seems to be sunk when all its volume is under the water surface.
The volume of the matress is V = 2.7*1.16*0.183 = 0.573 m3.
Fa = ρ*g*V ;
Archimedes force should be equal to the weight of the mattres with water:
ρ*g*V = mg+Mg
m = ρV - M = 1000 kg/m3 * 0.573 - 4.9 = 568.1 kg

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