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taurus [48]
2 years ago
12

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
Physics
1 answer:
Paul [167]2 years ago
8 0

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}.

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