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## AP®︎/College Physics 2

### Unit 1: Lesson 1

Density and Pressure

# Specific gravity

In this video David explains what specific gravity means. He also shows how to calculate the value for specific gravity and use it to determine the percent of an object that will be submerged while floating. Created by David SantoPietro.

## Video transcript

[MUSIC PLAYING THROUGHOUT] What does "specific gravity" mean? The specific gravity of an object is the density of that object divided by the density of water. The density of water is 1,000 kilograms per meter cubed. For instance, the density of gold is 19,300 kilograms per meter cubed. So the specific gravity of gold is 19.3. The density of ketchup is 1,400 kilograms per meter cubed. So the specific gravity of ketchup up is 1.4. Note, there's no units for specific gravity, because it's the ratio of one density to another density. So the units cancel each other out. OK, so why even bother defining something called the specific gravity? Well, one really cool thing about specific gravity is that, for something that floats, the specific gravity tells you the fraction of that object that will be below the water while it's floating. For instance, say you let a cube of wood with specific gravity 0.2 float in water. Since the specific gravity is 0.2, that means that 20% of the total volume of this wood is going to be submerged below the water while it's floating. If the cube of wood had a specific gravity of 0.6, 60% of the wood would be submerged beneath the water's surface. Ice has a density of about 920 kilograms per meter cubed. That means ice has a specific gravity of 0.92. And that's why 92% of an iceberg's volume is actually underneath the water. But what if we were to use a cube that had a density of 2,700 kilograms per meter cubed? The specific gravity would be 2.7, which means that 270% of this cube would be submerged beneath the water. But you can't have more than 100% of an object submerged. Even if the object were to sink, the maximum amount submerged would be 100%. So if the specific gravity of an object is greater than 1, that object is going to sink if placed freely in water. And it'll have exactly 100% of its volume submerged. Usually when people are referring to the specific gravity, they're referring to the density of the object divided by the density of water. But sometimes it's useful to define the specific gravity with respect to a liquid that's different from water. For instance, if you were to let some wood of density 638 kilograms per meter cubed float in oil that has a density of 850 kilograms per meter cubed, you could still find the percent of the wood that's submerged underneath the oil. Just use the density of oil instead of the density of water in the specific gravity formula. If we do that, we'll find that the wood does float in this oil with 75% of the wood's volume submerged beneath the surface of the oil. [MUSIC PLAYING]