How Much Weight Can a 2.8 kg Air Mattress Support in Water Before Sinking?

In summary, in order to determine the mass that a rectangular air mattress can support in water before sinking, we need to use the equations for density, buoyant force, and weight. The density of the object needs to be compared to the density of the fluid, in this case water, and the weight of the object needs to be compared to the buoyant force. By using these equations and knowing the dimensions and weight of the air mattress, we can calculate the maximum supported mass.
  • #1
b0r33d
6
0

Homework Statement



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


Homework Equations



Density = Mass / Volume
Magnitude of buoyant force = Weight of fluid displaced
Buoyant force = weight of floating object
Weight of object x Buoyant force = Density of object / Density of fluid
Density of water = 1000 kg/m3

The Attempt at a Solution



I can't figure out what I would need to do in order to answer the question or what I would need to find.
 
Physics news on Phys.org
  • #2
Hello bor, you need to try a bit so that we can help :smile:
 
  • #3


I would approach this problem by first understanding the concept of buoyancy and how it relates to the weight and volume of an object. The buoyant force is the upward force exerted on an object immersed in a fluid, and it is equal to the weight of the fluid that the object displaces. In this case, the fluid is water and the object is the air mattress.

To determine the mass that the air mattress can support before sinking, we need to calculate the buoyant force it experiences in water. This can be done by using the equation: Buoyant force = weight of fluid displaced. In this case, the weight of the fluid displaced is equal to the weight of the air mattress itself.

To calculate the weight of the air mattress, we can use the equation: Weight = mass x gravity. Plugging in the given values, we get: Weight = 2.8 kg x 9.8 m/s^2 = 27.44 N.

Since the air mattress is fully submerged in water, the buoyant force acting on it is equal to its weight. Therefore, the buoyant force is also 27.44 N.

To determine the mass that the air mattress can support in water before sinking, we need to use the equation: Weight of object x Buoyant force = Density of object / Density of fluid. Rearranging this equation to solve for the mass of the object, we get: Mass of object = (Density of object / Density of fluid) x Buoyant force. The density of water is 1000 kg/m^3, and the density of the air mattress can be calculated by dividing its mass by its volume (0.100 m x 0.500 m x 2.00 m = 0.1 m^3). So the density of the air mattress is 28 kg/m^3.

Plugging in the values, we get: Mass of object = (28 kg/m^3 / 1000 kg/m^3) x 27.44 N = 0.77 kg.

Therefore, the air mattress can support a mass of 0.77 kg in water before sinking. Any additional mass added to the air mattress would cause it to sink due to the increase in weight exceeding the buoyant force acting on it.
 

FAQ: How Much Weight Can a 2.8 kg Air Mattress Support in Water Before Sinking?

What is the buoyant force of an air mattress?

The buoyant force of an air mattress is the upward force exerted by the surrounding air on the mattress, which allows it to float on the surface of the water.

How is the buoyant force of an air mattress calculated?

The buoyant force of an air mattress can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object. In the case of an air mattress, the fluid is air and the weight of the air displaced is equal to the weight of the mattress.

Does the buoyant force of an air mattress change with the weight of the person on it?

No, the buoyant force of an air mattress does not change with the weight of the person on it. This is because the buoyant force is determined by the volume and weight of the mattress, not the weight of the person on it.

How does the temperature affect the buoyant force of an air mattress?

The temperature does not have a significant effect on the buoyant force of an air mattress. However, as the temperature increases, the air inside the mattress expands, causing it to become less dense. This can lead to a slightly higher buoyant force, but the difference is minimal.

Can the buoyant force of an air mattress be increased?

Yes, the buoyant force of an air mattress can be increased by increasing its volume. This can be done by adding more air to the mattress, which will displace more air and increase the buoyant force. However, it is important to not overinflate the mattress as it can become unstable and prone to popping.

Back
Top