An air mattress is 2.36 m long, 0.640 m wide, and 12.2 cm deep. If the air mattress itself has a mass of 0.252 kg, what is the maximum mass it can support in fresh water?

Vm = 2.36 * 0.640 * 0.122 = 0.1843 m^3=

Vol. of the mattress.

Dw=(0.252+x)/0.1843=1000kg/m^3.=Density of water.

(0.252+x)/0.1843 = 1000.
0.252 + x = 184.3
X = 184.3 - 0.252 = 184.05 kg = max. mass it can support.

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

The buoyant force is equal to the weight of the displaced water, which is given by the formula: Buoyant force = density of water * volume of water * gravitational acceleration

First, we need to determine the volume of water displaced by the air mattress. The volume can be calculated by multiplying the length, width, and depth of the mattress. However, before calculating the volume, we need to convert the given measurements from meters and centimeters to the same unit. Let's convert the measurements to meters:

Length of the air mattress = 2.36 m
Width of the air mattress = 0.640 m
Depth of the air mattress = 12.2 cm = 0.122 m

Now we can calculate the volume of water displaced:

Volume of water displaced = length * width * depth
Volume of water displaced = 2.36 m * 0.640 m * 0.122 m

Next, we know the density of water is approximately 1000 kg/m^3. Using this value, we can calculate the buoyant force:

Buoyant force = density of water * volume of water * gravitational acceleration
Buoyant force = 1000 kg/m^3 * (2.36 m * 0.640 m * 0.122 m) * 9.8 m/s^2

Finally, the maximum mass that the air mattress can support in fresh water is equal to the buoyant force divided by the gravitational acceleration:

Maximum mass = Buoyant force / gravitational acceleration
Maximum mass = (1000 kg/m^3 * (2.36 m * 0.640 m * 0.122 m) * 9.8 m/s^2) / 9.8 m/s^2

Simplifying this expression, we get:

Maximum mass = 1000 kg/m^3 * 2.36 m * 0.640 m * 0.122 m

Thus, by calculating this expression, you will find the maximum mass that the air mattress can support in fresh water.