Mass, Weight, Volume, Density, and Specific Gravity

Mass, weight, volume, density and specific gravity. These are all important terms that you’ll find in Physics and it’s important that you know the difference between each one.

First, we have mass, mass is a measure of the amount of substance in an object. How many atoms or molecules of that one substance are in a specific object? That’s what your mass is.


Question 1: The formula for the volume of a sphere is
Question 2: Density is a measurement


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The transcript is for your convenience.
Weight is a measure of the gravitational pull of earth on an object, so let’s look at our example over here. We have this rectangular prism and it measures 8 centimeters long, three centimeters wide, five centimeters high, so it’s mass I’m just going to tell you is 10 grams. Its weight is one pound and in the United States we measure weight in pounds, other countries have different units of weight. But pretty much all the scientific community is going to use grams and the metric system is units for mass.

10 grams tells us that we’ve got 10 grams of a substance in this box. The weight says that we have one pound of gravitational pull of earth on that box. Now, this is the gravitational pull of earth, which means that on different planets or different entities in our solar system, the weight would be different. For instance, on the moon, there is less than a gravitational pull, so your weight would be lower on the moon. On other planets that are further away or closer to the sun, you’re going to have a different gravitational pull.

You would weigh more or less on different planets, because the pull would be different, but whenever you see a weight listed, it’s going to be the gravitational pull of earth on an object, because that’s where you’re most likely to find these things.

We move on to volume. Volume is the measure of the amount of space occupied and there are many formulas to determine volume. It’s going to depend on what shape your object is, how you’re going to determine its volume. For instance, the volume of a cube is the length of one side cubed or s2, side cubed and the volume of a rectangular prism, is length times width times height or L times W times H. And in fact that is the same formula you could use for a cube, one side times one side, times one side.

Just in a cube it wouldn’t matter which side you picked, because they’re all the same length. And in a rectangular prism, it’s important to make sure you take the length of a side the length of the prism,  times the width of the prism, times the height of the prism. You can’t just pick any three sides. The volume of an irregular shape can be determined by how much water it displaces. Say you have a rock and you want to know the volume of this rock is, how much space does it take up, well, most of the time, a rock is not going to make a perfect sphere, so you can’t use that formula.

It’s not going to make a perfect rectangular prism or cube, unless it is formed that way and ground down to be a specific size, most of the time you’re going to find an irregularly shaped rock. Let’s look at how water displacement can help us with volume. If you fill a beaker with some water, let’s say we start with 20 milliliters of water, then we drop our rock into the same beaker and now our water reads 47.5 milliliters. Well you didn’t add any more water, what you added was the rock, so the difference between the new volume and the old volume is going to be the volume of your irregular object.

Our rock that we dropped into the water, we can take our new volume, subtract our old volume and it’s going to tell us the volume of our rock, our irregular object, so the new volume was 47.5 milliliters,  the old volume is 20 milliliters and so we take our new volume of 47.5 minus the old of 20 and get 27.45 milliliters. That would tell you the volume of this rock and there are different units of volume as well. It is not always given in the same units that width and height and length would be given in, but it can be given in more of a liquid measure since we did measure it this way.

Now, let’s come back to our example and find our volume, so our volume is going to be length times width, times height, so let’s take those. Eight centimeters long times three centimeters wide, times five centimeters tall, alright. Eight times three is 24 and then we have to multiply times five, five time four is 20, five times two is 10, plus two is 12 and so we get 120 centimeters cubed.

Whenever we multiply the centimeters out, it turned into centimeters squared and then centimeters cubed,  so your answer for volume is going to be given in cubic units and so this is a 120 cubic centimeters or centimeters cube that is our volume of this object. Now, let’s move on to you density. Density is a measure of the amount of mass per unit volume, so they want to know how much substance is there per the space that it makes up. Some things are going to be more dense, their particles are going to be smashed more closely together in a smaller unit of volume or some are going to be more spaced out and they’re going to be in a bigger unit of volume.

Density is going to tell us how much mass there is per volume, per space that an object is taking up. The formula for density is mass divided by volume or D equals M divided by V and it is given in terms of mass per cubic unit,  such as grams per cubic centimeter, grams per cubic centimeter. Let’s find the density of our object over here, so we have our mass, which is 10 grams  and we have our volume, which is the 120 cubic centimeters. Now, we just have to reduce and what we’re going to end up with is being able to cross out these zeros and we’re going to have one twelfth gram per cubic centimeter.

And we can turn that into a decimal, because that’s usually how we like to see things, so I’m going to do the division up here. We’ve got eight times 12 is 96, we’ve got four left over, 12 goes into 40 3 times so we get 36 and this is going to keep on repeating. We’ve put another zero and come down where you get 40 again, so its point 083 and it’s going to repeat. We’re just going to go to three units, so our density would equal to 0.083 grams per cubic centimeter. Okay, so our object has a density of 0.083 grams per cubic centimeter, that was based on its mass of 10 grams for a volume up to 120 cubic centimeters.

Next let’s move on to specific gravity, specific gravity is a measure the ratio of the substances density  compared to the density of water. This specific gravity of a substance would be
the density  of the substance divided by the density of water. Now, the density of water at room temperature is 1.000 grams per cubic centimetre. If you divide anything by one, it’s going to be itself, so as long as you’re at room temperature, the specific gravity of an object is basically going to be its density. But, as water gets cooler or hotter, its specific gravity is going to change a little bit and so specific gravity can change based on air pressure, based on temperature, based on any other physical elements that are going on in the area where you’re trying to determine specific gravity.

Water isn’t always going to be one gram per centimeter cube, but at room temperature it will be and so as long as everything’s at room temperature, regular pressure, then you’re going to have your specific gravity be basically the same as your density of the substance. Now, if your specific gravity is greater than that of water, so it’s greater than one gram per centimeter cube, then your substance is going to sink. It is denser than water, it’s going to stink below the water. If your specific gravity is less than water, then your substance will float. It has a specific gravity that’s less than water, it is less dense than the water, so it’s going to float. For instance, if you put most metal, if you put a penny in water, it’s going to sink, because it has a higher specific gravity than water.

But, if you have at piece of wood, it’s usually going to float, because it’s going to have a lower specific gravity than water. If the specific gravity of a substance is one or right out one, then it will be buoyant, so it will kind of bob around the top of the water. It won’t float right above it, it won’t sink to the bottom, it will bob right around the top. Let’s look at the specific gravity of our box over here, so we’ve got our density of the substance which is 0.083 grams per cubic centimeter and we have water, which is 1.000 grams per cubic centimeter. Your specific gravity would just be 0.083 grams per centimeter cube, because at room temperature water is going to be one and dividing by one is going to get you the same thing. With this one our box here, will it sink or float? Is the specific gravity less than that of water or greater than that of water? It’s less than that of water, less than specific gravity of water, so when it’s less than that of water, it’s going to float.

Let’s review all of these terms and make sure we understand the difference. The mass of our box was how much substance was in there, we had 10 grams of a substance in this shape. It weighed one pound, that was how much gravitational pull earth had on the object. Its volume was based on its actual size, how much space it occupied and it came out to 120 centimetres cubed and we got that by multiplying by length, by width by height. Its density was mass divided by volume, so our mass of 10 grams divided by volume of a 120 centimetres and we rounded that to point 083 grams per centimeter cubed.

Because we’re going to keep repeating forever with that three and then the specific gravity was just point 0.083 grams per cubic centimeter as well, because at room temperature water is one gram per centimeter cubed as well and the density isn’t going to change very much. The specific gravity is just going to be the same as the density. Since our objects specific gravity was less than that of water,  we know that it will float.

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