# Density

Density is a way to measure how tightly packed a material is. It's calculated by dividing the mass of the material by its volume. This is really helpful when we're talking about the different forms that matter can take: gas, liquid, and solid.

If we take a gas and put it in a container, the particles will spread out to fill the whole space. But if we take that same gas and turn it into a liquid, the particles will be more closely packed. And if we turn it into a solid, the particles will be packed together even more tightly.

We can use density to describe how much of a substance is in a fixed amount of space. Gases are least dense, because they have the least amount of mass in that space. Liquids are a bit more dense, because they have more mass in the same amount of space. And solids are the most dense, because they have the most mass in that same space. This is really important when we're trying to understand how different materials behave!

## What affects density?

Density is affected by various factors.

When we heat up a substance, it tends to expand. This means that as temperature increases, density decreases. On the other hand, when we cool a substance down, it becomes more dense.

Pressure also affects density. When we apply more pressure to a substance, it can cause the volume to decrease, which in turn increases the density. The opposite is also true - if we decrease the pressure, the volume can increase and the density will decrease.

It's interesting to note that humidity is inversely proportional to density. This means that when density decreases, humidity increases. So if we cool down a substance, its density will increase and its humidity will decrease.

## What is the formula for density?

The density of the fluid can be calculated using the formula:

ρ = m/V

Where:

ρ = density

m = mass

V = volume

Therefore, the density of the fluid is:

ρ = 1800 g / (235 ml x 0.001 L/ml)

ρ = 7.66 g/L

## What is upthrust?

Upthrust is an important concept in fluid mechanics, as it explains the buoyancy of objects when submerged in a fluid. When an object is submerged in a fluid, it experiences an upward force called upthrust. This force is equal to the weight of the fluid that is displaced by the object. This concept is known as Archimedes' principle.

Mathematically, the upthrust force can be expressed as:

Fup = ρVg

Where:

Fup = upthrust force

ρ = density of the fluid

V = volume of the object submerged in the fluid

g = acceleration due to gravity

The weight of the object can be expressed as:

W = mg

Where:

W = weight of the object

m = mass of the object

g = acceleration due to gravity

Using Archimedes' principle, we can equate the upthrust force to the weight of the fluid displaced by the object. Therefore:

Fup = W

ρVg = mg

V = m/ρ

Substituting V into the equation for upthrust force gives:

Fup = ρVg = ρ(m/ρ)g = mg

Therefore, the upthrust force is equal to the weight of the object when it is submerged in a fluid.

In summary, upthrust is the upward force experienced by an object when it is submerged in a fluid, and it is equal to the weight of the fluid that is displaced by the object. Archimedes' principle is used to explain this phenomenon and mathematically, the upthrust force can be expressed as the product of the fluid density, volume of the object and acceleration due to gravity.

**How is upthrust related to density?**

Upthrust is directly proportional to the density of the fluid. The difference between the density of a body submerged in a fluid and the density of that fluid determines whether the object sinks or floats. The diagram below shows when an object sinks or floats when submerged in fluid.

To calculate the acceleration of the object when it is sinking, we can use the following steps:

- Compare the weight of the object with the upthrust force to determine whether the object is sinking or floating. Since the object is sinking, the weight must be greater than the upthrust force.
- Use Newton's second law to analyze the forces acting on the object. Replace the weight with the product of mass and acceleration due to gravity, and the upthrust force with the product of density, acceleration due to gravity, and volume. This gives us the following equation:

m * a = ρ * g * V

Where:

m = mass of the object

a = acceleration of the object

ρ = density of the fluid

g = acceleration due to gravity

V = volume of the object

- Substitute the density of the object, which is four times the density of the fluid, into the equation. This gives us:

m * a = 4 * ρ * g * V

- Use the relationship between density, mass, and volume to substitute the mass term in the equation. This gives us:

ρobj * Vobj * a = 4 * ρ * g * V

Where:

ρobj = density of the object

Vobj = volume of the object

- Substitute each term that contains ρobj with 4ρfluid, using the relation that was obtained earlier. This gives us:

4 * ρfluid * Vobj * a = 4 * ρ * g * V

- Divide both sides by the common terms which are ρfluid and V. This gives us:

4 * a = ρ * g

- Solve for acceleration. This gives us:

a = (ρ * g) / 4

Substituting g with the acceleration due to gravity constant, 9.81 m/s2, we get:

a = (ρ * 9.81) / 4

Therefore, the acceleration of the object when it is sinking is equal to (ρ * 9.81) / 4, where ρ is the density of the fluid in kg/m3.

## Density

**What is density equal to? **

Density is equal to the mass over volume: F=m/V.

**What is density used to describe in science? **

Density can be used to describe how dense a substance is.

**Does temperature affect density? **

Yes, temperature and density are inversely proportional.

**What does low density mean? **

Low density means that the particles of a material are loosely packed.

**What does high density mean? **

High density means that the particles of a material are tightly packed.