Question

A twin-sized air mattress used for camping has dimensions of 75 cm by 225 cm by 17.5 cm when blown up. The weight of the mattress is 2 kg How heavy a person, in newtons, could the air mattress support if it is floating in freshwater, with density1000 kg/m^3?

Answer 1

2870 N

Step-by-step explanation:

There are three forces on the mattress. Weight of the mattress, weight of the person, and buoyancy.

∑F = ma

B - mg - Mg = 0

Buoyancy is equal to the weight of the displaced fluid.

ρVg - mg - Mg = 0

ρV - m = M

Plugging in values:

M = (1000 kg/m³) (0.75 m × 2.25 m × 0.175 m) - 2 kg

M = 293 kg

The person's weight is therefore:

Mg = 293 kg × 9.8 m/s²

Mg = 2870 N