Calculating Buoyancy Force for Iron Cube Submerged in Water | Homework Solution

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In summary, a 20x20x20 cm^3 cube made of iron with a density of 7860kg/m^3 is completely submerged in water with a density of 1000kg/m^3. The buoyancy force acting on the cube can be found by calculating the weight of the water displaced by the cube, which would be less than 8x10^7 Newtons. The average density of a person is also close to 1000 kg/m^3, and a person is bigger than the cube, so the weight of the cube cannot be 8x10^7 Newtons.
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Homework Statement


A cube made from iron has sides equal to 20cm/side. The density of iron is 7860kg/m^3. The cube is completely submerged in water; the density of water is 1000kg/m^3. What is the buoancy force acting on the cube.


Homework Equations


W(DL)= (D(L))(V)(g)


The Attempt at a Solution


W(DL)=(1000kg/m^3)(8000cm^3)(10m/s^2) =8x10^7 Neutons
Im not sure if this answer is correct ?
 
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  • #2
Take care of your dimensions. You're using the density in kg per meter^3, but volume in cm^3.
1 Newton is 1 [itex]kg m s^{-2}[/itex] You can get the right units from there.
When in doubt, always use SI-units.
 
  • #3
Force of buoyancy = weight of the water displaced by the cube. How can that small cube of water weight 8x10^7 Newtons?

Think, what is your weight? less or more than 8x10^7 N? Your average density is also very close to 1000 kg/m^3. Are you bigger or smaller than that 20x20x20 cm^3 cube?


ehild
 

1. What is buoyancy force?

Buoyancy force is the upward force exerted by a fluid on an object placed in it. It is equal to the weight of the fluid displaced by the object.

2. How is buoyancy force calculated?

Buoyancy force is calculated using Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid it displaces. This can be represented by the equation Fb = ρVg, where Fb is the buoyancy force, ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity.

3. What factors affect buoyancy force?

The buoyancy force on an object is affected by the density of the fluid, the volume of the displaced fluid, and the acceleration due to gravity. It is also affected by the shape and size of the object, as well as the depth at which it is submerged in the fluid.

4. How does buoyancy force relate to an object's weight?

The buoyancy force on an object is equal to the weight of the fluid it displaces. If the buoyancy force is greater than the object's weight, it will float. If the buoyancy force is less than the object's weight, it will sink.

5. Why do some objects float while others sink?

Objects float or sink based on their density compared to the density of the fluid they are placed in. If the object's density is less than the fluid's density, it will float. If the object's density is greater than the fluid's density, it will sink.

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