Question

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.

Answer 1

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