Question

A twin-sized air mattress used for camping has dimensions of 100 cm by 194 cm by 14 cm when blown up. The weight of the mattress is 4 kg. How heavy a person (in N) could the air mattress hold if it is placed in freshwater

Answer 1

Answer:

$2625.156\ \text{N}$

Explanation:

Dimensions of mattress 100 cm by 194 cm by 14 cm

$m_m$ = Mass of mattress = 4 kg

$\rho$ = Density of water = $1000\ \text{kg/m}^3$

g = Acceleration due to gravity = $9.81\ \text{m/s}^2$

Volume of mattress

$V=100\times 194\times 14=271600\ \text{cm}^3=0.2716\ \text{m}^3$

Weight of water displaced is equal to the buoyant force

Mass of water

$m=\rho V\\\Rightarrow m=1000\times 0.2716\\\Rightarrow m=271.6\ \text{kg}$

Mass of person would be

$m_p=m-m_m=271.6-4\\\Rightarrow m_p=267.6\ \text{kg}$

Weight of the person would be

$w=m_pg\\\Rightarrow w=267.6\times 9.81\\\Rightarrow w=2625.156\ \text{N}$

The air mattress could hold a person that weighs up to $2625.156\ \text{N}$.