How Much Additional Mass Can a Floating Air Mattress Support?

[mizzy]

Homework Statement

A rectangular waterproof air mattress is 2.0m long, 0.50mwide and 0.08m thick. It has a mass of 2.0kg and is supporting an additional mass of m, while floating in the water,
calculate the mass, m, assuming the density of water is 1000kg/m^3 and density of air is 1.29kg/m^3

Homework Equations

B = weight of displaced fluid

B= density of water x volume * g

where B = mass of 2kg, unknown mass and mass of air

The Attempt at a Solution

I solved it and i got 78.1kg. The answer is 79.9kg

this is what i did:

m1g + m2g + density(air) * V *g = density(water) * V * g

solve for m2:

m2 = density(water) * V - density(air) * V - m1
m2 = 1000(0.08) - 1.29(0.08) - 2
m2 = 78.1kg

Can someone point out where i went wrong?

 

[Borek]

No idea how to get answer that you listed as correct, IMHO it is off by 2 kg, but

m2 = 1000(0.08) - 1.29(0.08) - 2
m2 = 78.1kg

this is just incorrect. Perhaps you have rounded down intermediate results, or just keyed those numbers wrong in your calculator.

800 - 0.1032 - 2 = 77.8968 ≈ 77.9