A 2.8 kg rectangular air mattress is 2 meters long,.5 meters wide, and .1 meter thick what mass can't support 50% submerged.
V = 2 * 0.5 * 1 = 1 m^3.
Vs = 0.5 * 1m^3 = 0.5 m^3 = Vol. surmerged.
Mass = 0.5m^3 * 100kg/m^3 = 50 kg = mass of water displaced.
Mass = 50 - 2.8 = 47.2 kg = Mass it can
support when 50% surmerged.
To calculate the maximum mass the air mattress can support while being 50% submerged, we need to consider the buoyant force acting on it.
First, let's calculate the volume of the air mattress:
Volume = length × width × thickness
Volume = 2 m × 0.5 m × 0.1 m
Volume = 0.1 m³
The buoyant force acting on an object submerged in a fluid can be calculated using Archimedes' principle:
Buoyant force = Density of fluid × Volume displaced × gravity
Assuming the air mattress is submerged in water, the density of water is approximately 1000 kg/m³, and the acceleration due to gravity is 9.8 m/s².
Substituting the values into the formula:
Buoyant force = 1000 kg/m³ × 0.1 m³ × 9.8 m/s²
Buoyant force = 980 N
At 50% submersion, the buoyant force is equal to half the weight of the object.
Let's denote the maximum mass the air mattress can support as "m".
Weight of the air mattress = mass × gravity
Weight of the air mattress = 2.8 kg × 9.8 m/s²
Weight of the air mattress = 27.44 N
Setting up the equation for buoyant force:
Buoyant force = (1/2) × Weight of the air mattress
980 N = (1/2) × 27.44 N × gravity
Solving for gravity:
gravity = 980 N / ((1/2) × 27.44 N)
gravity ≈ 71.18
Now, we can calculate the maximum mass the air mattress can support using the formula:
Weight of the air mattress = mass × gravity
27.44 N = m × 71.18
m ≈ 0.385 kg
Therefore, the maximum mass the air mattress can support while being 50% submerged is approximately 0.385 kg.
To find out the maximum mass that the rectangular air mattress can support while being 50% submerged, we need to consider the principle of buoyancy and Archimedes' principle.
Archimedes' principle states that the buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Let's calculate the volume of the air mattress first:
Volume = length x width x thickness
Volume = 2 m x 0.5 m x 0.1 m
Volume = 0.1 cubic meters
Since the air mattress is 50% submerged, it displaces an equal volume of water. So the volume of water displaced is also 0.1 cubic meters.
Now, let's calculate the weight of this displaced water:
Density of water = 1000 kg/m^3 (approximately)
Weight of displaced water = density x volume x gravity
Weight of displaced water = 1000 kg/m^3 x 0.1 m^3 x 9.8 m/s^2
Weight of displaced water = 980 N
According to Archimedes' principle, the buoyant force acting on the submerged object is equal to the weight of the displaced water, which is 980 N.
Now, we need to find the maximum mass that the air mattress can support. We can use the equation:
Weight = mass x gravity
Rearranging the equation, we have:
Mass = weight / gravity
Mass = 980 N / 9.8 m/s^2
Mass = 100 kg
Therefore, the maximum mass that the rectangular air mattress can support while being 50% submerged is 100 kg.