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

`2625.156\ \text{N}`

Step-by-step 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* 194* 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* 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* 9.81\\\Rightarrow w=2625.156\ \text{N}`

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