How to Calculate the Density of Solids or Liquids

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  • 0:01 What Is Density?
  • 0:42 Calculating Density of…
  • 2:40 Example Problem
  • 5:01 Lesson Summary
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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.

What Is Density

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.

Calculating Density of Solids or Liquids

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).

Example Problem

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.

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