Question

A twin-sized air mattress used for camping has dimensions of 100 cm by 200 cm by 15 cm when blown up. The weight of the mattress is 2 kg. How heavy a person could the air mattress hold on top?

Answer 1

This has to do with buoyant force. Essentially this force is equal to the amount of liquid displaced (called Archimedes Principle). The density of water is 1000kg/m^3.

The essence of this question is really asking if the volume of the mattress is displaced what weight of water is equal to or less than the weight of the person. Let’s get some numbers in here.

First convert it all to meters. 1m x 2m x 0.15m. Now find volume. LxWxH = 0.3 cubic meters (m^3).

Now if you multiply the volume by the density of water you get:

1000x 0.3 = 300kg <-- this is the weight of 0.3 cubic meters of water.

Since the mattress itself weighs 2kg (I assume this includes the weight of the air inside. 1.275kg/m^3 if you need to do that separately) you have to subtract this from the total giving you:

300-2 = 298kg.