A 2.8 kg rectangular air mattress is 2.00m long,0.500 m wide and 0.100m thick. What mass can it support in water before sinking?

M= 97.2kg

To find the mass that the air mattress can support in water before sinking, we need to calculate the buoyant force acting on the air mattress.

The buoyant force is equal to the weight of the water displaced by the submerged part of the object.

To calculate the volume of water displaced, we need to find the volume of the submerged part of the air mattress.

Given:
Length of the air mattress (l) = 2.00 m
Width of the air mattress (w) = 0.500 m
Thickness of the air mattress (h) = 0.100 m

Volume of the submerged part = l * w * h

Substituting the values, we get:
Volume of the submerged part = 2.00 m * 0.500 m * 0.100 m

Next, we need to find the density of water.

The density of water is approximately 1000 kg/m³.

Now, we can calculate the mass of the water displaced by the submerged part of the air mattress.

Mass of water displaced = density of water * volume of the submerged part

Substituting the values, we get:
Mass of water displaced = 1000 kg/m³ * (2.00 m * 0.500 m * 0.100 m)

Finally, the maximum mass that the air mattress can support before sinking is equal to the mass of the water displaced.

So, the air mattress can support a maximum mass of:
Mass = Mass of water displaced

Calculating the values, we find the maximum mass supported by the air mattress in water before sinking.

Figure out its volume.

Then, figure out the weight of the water that volume would displace

weight displaced water= volume*density*g
bouyance=weight water displaced-2kg*9.8N/kg

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