A 1.8 kg rectangular air mattress is 2.46 m long, 1.23 m wide, and 0.189 m thick.
What mass can it support in water before sinking?
Answer in units of kg.
(1000 kg/m^3 * volume) - 1.8 kg
570.0762 kg
To find the mass that the air mattress can support in water before sinking, we need to determine its buoyancy force. Buoyancy force is the upward force exerted on an object submerged in a fluid, in this case, water.
The buoyancy force can be calculated by multiplying the density of water (ρ) by the volume of the displaced water. The volume of the displaced water can be determined by multiplying the area of the air mattress (A) by the depth submerged (h).
Let's first find the area (A) of the air mattress. The area is calculated by multiplying the length (l) by the width (w):
A = l * w
Substituting the given values:
A = 2.46 m * 1.23 m
Next, let's calculate the volume (V) of the displaced water. The volume is calculated by multiplying the area (A) by the depth submerged (h):
V = A * h
Substituting the given values:
V = (2.46 m * 1.23 m) * 0.189 m
Now, we need to find the density of water (ρ). The density of water is approximately 1000 kg/m³.
Finally, we can calculate the buoyancy force (Fb) exerted on the air mattress:
Fb = ρ * V
Substituting the given values:
Fb = 1000 kg/m³ * (2.46 m * 1.23 m) * 0.189 m
Now, we know that the buoyancy force is equal to the weight of the water displaced by the air mattress when it is fully submerged. Therefore, the mass that the air mattress can support in water before sinking is equal to the mass of the displaced water.
The mass of the displaced water (m_water) can be calculated by dividing the buoyancy force (Fb) by the acceleration due to gravity (g ≈ 9.8 m/s²):
m_water = Fb / g
Substituting the given values and calculating:
m_water = (1000 kg/m³ * (2.46 m * 1.23 m) * 0.189 m) / 9.8 m/s²
Now, we can solve for the mass of the water (m_water):
m_water ≈ 6.78 kg
Therefore, the air mattress can support approximately 6.78 kg of mass in water before sinking.