Buoyant force of air mattress

[b0r33d]

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.

 

[luben]

Hello bor, you need to try a bit so that we can help

 

[Moetasim]

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.