# Floating, hydrostatic forces, average density

• fog37
In summary, the shape of the object (in this case, the boat) affects the amount of weight it can displace and therefore the buoyancy force it has.
fog37
Hello Forum,
I am revisiting Archimedes principle and its important consequences.
I am aware that a cube (homogeneous) made of iron will always sink in water regardless of its mass. If we changed the iron cube into a different shape (cone, cylinder, prism, parallelepiped, etc.), the object would still sink. However, there are some possible transformations that can morph the iron cube into something that is able to float. This is often explained by saying that the "average' density of the object has become lower than the water density due to the inclusion of areas of emptiness in the calculation of the total volume. That is a good explanation but it hides a lot of interesting details. Essentially, I would like to gain a more detailed and qualitative understanding of why an iron cube sinks while a ship of the same mass floats. Archimedes force is the vertical upward directed component of net force which derives from the vectorial sum of the all the hydrostatic elementary normal forces acting on the surface of the immersed object. From the perspective of the hydrostatic normal force distribution that water exerts, what is different in the hydrostatic force distribution for the iron cube and for the iron boat? The mass, hence the weight is the same. The change in shape essentially leads to a redistribution of the mass. A computer calculation can provide the accurate answer but does anyone have some insight in what happens when we transform a homogenous sinking object into something (like a basin) that can float?

Thanks for any thoughts!

You just need its [under water] shape to be such that the body can displace more weight of water than its own weight, then it will float.

Last edited:
Nidum
One key difference between a boat and something that is almost a boat is that a boat does not leak.

Nidum
fog37 said:
I would like to gain a more detailed and qualitative understanding of why an iron cube sinks while a ship of the same mass floats.
Because the ship displaces more water.

fog37 said:
I am aware that a cube (homogeneous) made of iron will always sink in water regardless of its mass. If we changed the iron cube into a different shape (cone, cylinder, prism, parallelepiped, etc.), the object would still sink. However, there are some possible transformations that can morph the iron cube into something that is able to float.

Have you considered morphing a solid cube into a hollow cube enclosing much more volume with the same mass?

Thanks everyone.

I see how one shape (the boat shape) must displace more water than the cube because that larger displaced mass of water corresponds to a larger buoyancy force. But I would like to understand, from a qualitative point of view, why that happens for the hull shape. The elementary forces add up to a larger vertical push (Archimedes force)...

fog37 said:
But I would like to understand, from a qualitative point of view, why that happens for the hull shape. The elementary forces add up to a larger vertical push (Archimedes force)...

https://arxiv.org/pdf/1110.5264.pdf

## 1. What is the concept of floating?

The concept of floating is when an object is able to stay suspended in a liquid or gas without sinking. This is due to the buoyant force exerted by the liquid or gas on the object.

## 2. What is hydrostatic force?

Hydrostatic force is the force exerted by a fluid on an object that is submerged or partially submerged in the fluid. This force is a result of the pressure exerted by the fluid on the object.

## 3. How does the shape of an object affect its ability to float?

The shape of an object can affect its ability to float because it determines the amount of surface area that is in contact with the fluid. Objects with a larger surface area will experience a greater buoyant force and are more likely to float.

## 4. What is the average density of an object and how does it relate to floating?

The average density of an object is the mass of the object divided by its volume. This density determines whether an object will float or sink in a fluid. Objects with an average density less than the density of the fluid will float, while objects with a greater average density will sink.

## 5. How do you calculate the buoyant force on an object?

The buoyant force on an object can be calculated using the formula Fb = ρVg, where ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity. This formula applies for objects that are completely or partially submerged in a fluid.

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