Bouyant force on a cube floating at the surface between water and oil?

In summary, we are given a floating cube with dimensions of 15 cm, with 52% submerged in water and 48% submerged in oil. Using Archimedes' Principle and the buoyant force equation, we can calculate the mass of the cube to be 3.33 kg and the buoyant force on the cube to be 30 N.
  • #1
kalisious
13
0

Homework Statement


A cube of 15 cm is floating at the surface between water and oil. The oil has a density of 810 kg/m3. If the cube floats so that it is 52% in water and 48% in the oil, what is the mass of the cube and what is the buoyant force on the cube?


Homework Equations


Archimede's Principle
Fb= densityfluidvfluidg



The Attempt at a Solution


Not sure how to find the mass of the cube when only the height of one side is given?
 
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  • #2
The cube is displacing it's own weight in oil and water.
it might be simpler to think of it as two (almost ie 0.52/0.48) half cubes immersed in oil and water.
 
  • #3
fb = (1000*0.52+810*0.48)*0.15^3*9.8
=30 N

mass=fb/g
=30/9=3.33
 

FAQ: Bouyant force on a cube floating at the surface between water and oil?

What is the concept of bouyancy?

Bouyancy is the upward force exerted by a fluid on an object that is partially or fully submerged in it. This force is equal to the weight of the fluid that the object displaces, according to Archimedes' principle.

How does the bouyant force on a cube floating between water and oil differ from that of a cube floating in just water?

The bouyant force on a cube floating between water and oil is determined by the difference in densities between the two fluids. This results in a net downward force on the cube, making it float at a lower level than it would in just water. The bouyant force in this scenario is also affected by the relative heights of the two fluids.

What factors influence the magnitude of the bouyant force on a cube floating at the surface between water and oil?

The magnitude of the bouyant force is influenced by the densities of the two fluids, the relative heights of the fluids, and the size and shape of the object. The greater the difference in densities between the two fluids, the greater the bouyant force will be. The relative heights of the fluids also affect the bouyant force, with the cube experiencing a greater force if the water is at a higher level than the oil. Additionally, the size and shape of the cube will impact the bouyant force, with larger and more streamlined objects experiencing a greater force.

How can the bouyant force on a cube floating between water and oil be calculated?

The bouyant force can be calculated by multiplying the density of the fluid by the volume of fluid displaced by the object. In the case of a cube floating between water and oil, this would involve calculating the volume of the cube submerged in each fluid separately and then taking the difference between the two.

What happens to the bouyant force if the cube is compressed or stretched while floating at the surface between water and oil?

If the cube is compressed while floating, the volume of fluid it displaces will decrease, resulting in a decrease in the bouyant force. Conversely, if the cube is stretched while floating, the volume of fluid it displaces will increase, resulting in an increase in the bouyant force. This can affect the equilibrium of the cube and cause it to sink or rise in the fluid.

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