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Physical Science: Middle School9 chapters | 61 lessons

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Lesson Transcript

Instructor:
*David Wood*

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you will be able to explain what density is and calculate the density of solids or liquids from physical measurements. A short quiz will follow.

**Density** is a measure of how compact the mass in a substance or object is. The density of an object or substance can be calculated from this equation: density in kilograms per meter cubed is equal to mass in kilograms, divided by volume in meters cubed (*p* = *m / v*). So density could be described as the number of kilograms that 1 meter cubed of substance weighs.

When two materials are mixed together, the density is what determines which one will rise and which one will sink. This tells you whether objects sink or float and explains why cold fronts sink below warm fronts in weather patterns. Understanding density is an important step in understanding the world around us.

When you're asked to calculate density, you need to use a combination of the density equation we've already introduced and an understanding of volume. For example, you might not be given the actual volume of the material or object to put into the density equation. Instead, you may be given the measurements of the object and be expected to figure out the volume yourself.

The volume of a cube or cuboid is length times width times height (*L* * *W* * *H*). So if you needed to calculate the density of a cube, you would first measure the length of one of the sides. Let's say that the length of our cube turned out to be 3 meters. You would first need to calculate the volume by multiplying 3 by 3 by 3 (*V* = 3 * 3 * 3). You would also need to put the cube on a scale to measure its mass. Last of all, you would divide your volume by your mass to get the density of the cube (*p* = *m / v*).

But what if the material isn't a solid? What if it's a liquid?

Measuring the volume of a liquid isn't as obvious, because liquids change shape. When you measure liquids in a measuring jug, the numbers on the side are things like fluid ounces, pints, and liters (or milliliters). Liters are used in scientific equipment because those are standard scientific units. And there's a very good reason we use liters. Volume is measured in meters cubed, and 1 meter cubed is equal to 1,000 liters. So the conversion is super easy. (Also note that 1 liter is equal to 1,000 milliliters).

So to summarize, here are the steps to calculate the density of a solid or liquid:

1. Figure out the volume, by either measuring the dimensions of a solid or using a measuring jug for a liquid. Convert any units as needed to get a number in meters cubed.

2. Put the object or material on a scale and figure out its mass.

3. Divide the mass by the volume to figure out the density (*p* = *m / v*).

Okay, let's go through an example. Your best friend really likes milk, and one day you get curious. You wonder what the density of the milk he drinks is. Your friend lets you borrow his glass of milk to figure it out. You put the milk in a measuring jug and find that he has 150 milliliters of milk. Then you put it on a scale. The mass of the glass and the milk together is 0.115 kilograms, and the mass of the glass on its own is 0.1 kilograms. What is the density of the milk?

First of all, we should write down what we know.

- The volume of milk, Vmilk, is 150 ml.
- The mass of the glass and milk, mglass&milk, is 0.115 kg.
- And the mass of the glass on its own is 0.1 kg.

We know that density is equal to mass divided by volume (*p* = *m / v*), so we need to figure out the mass of the milk in kilograms and the volume of the milk in meters cubed.

Before we plug numbers into the equation, we need to do some separate calculations.

First of all, what is the mass of the milk? Well, the mass of the glass and the milk together is 0.115, and the mass of the glass on its own is 0.1, so the mass of the milk must be (0.115 - 0.1), which is 0.015 kilograms. Now we have our mass.

Next, we need the volume in meters cubed. We know the volume of milk is 150 milliliters, so we just need to convert this into meters cubed. There are 1,000 milliliters in a liter, so 150 ml is equal to 0.15 liters (150 / 1,000 = 0.15). You just divide by 1,000. And there are 1,000 liters in a meter cubed, so to get our number in meters cubed, you divide by 1,000 again. That gives us 0.00015 meters cubed (0.15 / 1,000 = 0.00015). And that's our volume.

So now we have the volume of the milk in meters cubed and the mass of the milk in kilograms. Plug those into the density equation: 0.015 kilograms divided by 0.00015 meters cubed gives us a density of 100 kilograms per meter cubed (0.015 / 0.00015 = 100). And that's it; that's our answer.

**Density** is a measure of how compact the mass in a substance or object is. The density of an object or substance can be calculated from this equation: density in kilograms per meter cubed is equal to mass in kilograms, divided by volume in meters cubed (*p* = *m / v*).

Here are the steps to calculate the density of a solid or liquid:

1. Figure out the volume by either measuring the dimensions of the solid or using a measuring jug for a liquid. Convert any units as needed to get a number in meters cubed.

2. Put the object or material on a scale to figure out its mass.

3. Divide the mass by the volume to figure out the density (*p* = *m / v*).

You may also need to know how to calculate the volume of a solid. For example, for a cube, volume is length times width times height (*V* = *L* * *W* * *H*). And you'll need to know some conversions. For example, 1,000 liters is 1 meter cubed, and 1000 milliliters is 1 liter.

After this lesson, you should have the ability to:

- Define density
- Explain how to calculate the density of a solid or liquid

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Physical Science: Middle School9 chapters | 61 lessons

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