# Problem that (probably) involves Archimedes' principle

• tsw99
In summary, the weight of a rectangular block is 15N and when a thin string is tied to its center, 25% of the block is submerged when the tension is 10N. Adding oil of density 800 kg/m^3 to the beaker increases the tension as it surrounds the block and exerts forces on each of the four side walls. This is because the buoyancy force increases as more of the block is now covered by oil.
tsw99

## Homework Statement

Serway book 14.26
The weight of a rectangular block is 15N. With a thin string, the center of the horizontal bottom face of the block is tied to the bottom of a beaker partly filled with water. 25% of the block is submerged when the tension is 10N

Oil of density 800 kg/m^3 is steadily added to the beaker and form a layer above the water and surronding the block. The oil exerts forces on each of the four side walls that the oil touches.

Explain what happens to the tension when oil is added?

## The Attempt at a Solution

I suggest the tension will increase by looking at the next question, but I really do not understand why the tension changes by adding oil. Not only the buoyancy changes because it also displaces some oil?

hi tsw99!
tsw99 said:
… I suggest the tension will increase by looking at the next question, but I really do not understand why the tension changes by adding oil. Not only the buoyancy changes because it also displaces some oil?

i assume that the string stays the same length, and the water stays the same volume, so the same amount of the block is "under" water, but some more of the block is now covered by oil

find the buoyancy force before, and the buoyancy force after

## What is Archimedes' principle and how does it relate to problems?

Archimedes' principle is a scientific law that states that the buoyant force acting on an object is equal to the weight of the fluid it displaces. This principle is often used to solve problems involving objects submerged in a fluid, such as water.

## What are some common examples of problems that involve Archimedes' principle?

Examples of problems that involve Archimedes' principle include calculating the buoyant force acting on a submerged object, determining the density of an object by measuring its buoyancy, and finding the volume of an irregularly shaped object by submerging it in a known fluid.

## How can Archimedes' principle be applied to real-life situations?

Archimedes' principle is used in many real-life situations, such as designing ships and submarines, calculating the weight of an object in water, and understanding the behavior of hot air balloons. It is also important in understanding how objects float or sink in different fluids.

## What are the key factors to consider when solving a problem involving Archimedes' principle?

When solving a problem involving Archimedes' principle, it is important to consider the density of the object and the density of the fluid it is submerged in. It is also necessary to take into account the volume of the object and the depth at which it is submerged.

## Are there any limitations to Archimedes' principle?

While Archimedes' principle is a useful tool for solving many problems, it does have some limitations. It assumes that the fluid is incompressible and that the object is completely submerged. It also does not take into account factors such as surface tension and the shape of the object. In some cases, more complex mathematical models may be necessary to accurately solve a problem involving buoyancy.

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