Buoyancy to find mass, density and force to submerge

In summary, a plastic cube with dimensions of 200mm x 200mm x 200mm is placed in a cylindrical container with a diameter of 400mm and filled with sea water with a density of 1024kg/m^3. The level of the water rises by 30mm as the cube floats. To find the mass and density of the cube, we must first calculate the volume of water displaced. For the extra downward force needed to submerge the cube completely, we can use the formula pgV(water displaced) - pgV(cube) = extra force. To calculate the volume of water displaced, we can use the sum of the original water volume and the submerged part of the cube. This can then be
  • #1
garrigues
2
0

Homework Statement


A plastic cube, 200mm x 200mm x 200mm, is left in a cylindrical container that has a diameter of 400mm holding sea water, density 1024kg/m^3. The level in the container increases by 30mm as the block floats.
i) Find the mass and density of the cube.
ii) Find the extra downward force needed to completely submerge the cube.

Homework Equations


V(water displaced)
p = m/v

The Attempt at a Solution


i) For the mass, I'm having trouble determining the V(water displaced). Is it 200x200x30mm or the volume of water risen - area of 400mm diameter x 30mm? I leaning towards the former, but then what is the point of mentioning the container diameter?
ii) Probably well wrong here, but is that: pgV(water displaced) - pgV(cube) = extra Force?
 
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  • #2
If the water were not displaced, then the cube would just be on its surface. But when water does get displaced, it goes up, so it is contained between the submerged part of the cube and the container walls.
 
  • #3
So is it the volume of water risen (Area of 400mm diameter x 30mm) minus 200x200xV(cube submerged)? Problem is, how do I know the V(cube submerged) if I don't have its density?

I'm thinking, calculate V(water displaced) -> calculate mass -> get density.

Thanks voko
 
  • #4
The cylindrical volume at the high water mark is the sum of the original water volume and the submerged part of the cube.
 
  • #5


To find the mass of the cube, we first need to calculate the volume of water displaced. This can be done by using the formula for the volume of a cylinder: V = πr^2h, where r is the radius (200mm/2 = 100mm) and h is the height of the water risen (30mm). So, V = π(100mm)^2(30mm) = 942,477mm^3.

Next, we can use the equation p = m/v to find the density of the cube. Plugging in the values, we get 1024kg/m^3 = m/0.000942m^3. Solving for m, we get a mass of approximately 0.96kg.

For the extra downward force needed to completely submerge the cube, we can use the equation F = pgV, where p is the density of the sea water (1024kg/m^3), g is the acceleration due to gravity (9.8m/s^2), and V is the volume of water displaced (0.000942m^3). Plugging in the values, we get F = (1024kg/m^3)(9.8m/s^2)(0.000942m^3) = 9.47N.

So, the extra downward force needed to completely submerge the cube is approximately 9.47N.
 

What is buoyancy?

Buoyancy is the upward force exerted by a fluid on an object that is partially or fully submerged in it.

How does buoyancy help us find mass?

Buoyancy can be used to find the mass of an object by determining the amount of water it displaces. The buoyant force is equal to the weight of the water displaced, which is also equal to the weight of the object. By measuring the buoyant force and the density of the fluid, we can calculate the mass of the object using the formula: mass = buoyant force / (density x acceleration due to gravity).

What is the relationship between buoyancy and density?

Buoyancy and density are directly related. The more dense an object is, the more it will sink in a fluid and the less buoyant force it will experience. Conversely, less dense objects will float more easily due to the greater buoyant force acting on them.

How can we use buoyancy to find density?

To find the density of an object, we can use the buoyant force and the volume of the object. The buoyant force is equal to the weight of the object, and the volume can be determined by measuring the amount of water displaced when the object is submerged. The density can then be calculated using the formula: density = buoyant force / volume.

What is the force required to submerge an object?

The force required to submerge an object is equal to the weight of the object minus the buoyant force acting on it. In other words, it is the force needed to overcome the buoyant force and push the object down into the fluid.

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