What additional mass can the water support in Kg?

Question

A rectangular air mattress is 2.2 m long, 0.49 m wide, and 0.10 m thick. If it has a mass of 2.0 kg, what additional mass can it support in water?

Answer 1

Fb = pVg

Fb = buoyancy force
p = density of water = 1000 kg / m³
V = the submerged volume of the mattress

To find the maximum mass the mattress can support, we'll have to "maximize" the submerged volume by saying that the mattress is completely submerged, and is about to sink.

Fb = pVg

Fb = (1000)(2.2 * 0.49 * 0.10)(9.80)

Fb = 1.1 x 10³ N (remember, only 2 sig. figs. are allowed because the value with the least number of sig. figs. had 2 of them)

In order to find the additional mass that can be added (Ma), I will set the buoyant force equal to the gravitational force, This means that the mattress is just barely floating:

Fb = Fb = 1.1 x 10³ N = mg

1.1 x 10³ N = 9.80m

m = 1.1 x 10² kg (this is the maximum mass that can be added)

The additional mass (Ma) that can be added = max. mass - 2.0 kg

Ma = 1.1 x 10² kg - 2.0 kg = 1.1 x 10² kg

*** The mattress in water can only support about 1.1 x 10² more kg of weight. If more weight is added after that, the mattress will sink.

*** I am pretty sure my answer is perfect (correct number of sig. figs.) but your teachers answer or the back-of-the-book's answer may be a little different.

Answer 2

Calculate the volume of the air mattress. Multiply by the density of water: 10^3 Kg/meter^3. The number of Kgs that gives you is the total mass the air mattress can support.

This additional mass, does it have any volume? You might need to consider that too.

Answer 3

guessing its something to do with denisty, find p of water and should be simple enough, or am i way of the ball