# Relationship between mass and volume graph

### How Are Density, Mass & Volume Related? | Sciencing

Mass, volume and density are three of an object's most basic properties. Mass is how heavy something is, volume tells you how big it is, and. What is the relationship between mass and volume for a copper cylinder. From our graph we can tell that there is a positive linear relationship between volume. However, the relationship between mass and volume is constant for a substance at a given temperature and pressure. This relationship.

As with mass, increasing and decreasing the amount of material also increases and decreases the volume of the substance. For example, 10 grams of freshwater has a volume of 10 milliliters.

**Density and Slope Graphing by Mr. Chesbro**

Unlike mass and volume, increasing the amount of material measured does not increase or decrease density. This makes density a useful property in identifying many substances. However, since volume deviates with changes in temperature and pressure, density can also change with temperature and pressure. Specific Gravity One derivative measurement of density is specific gravity. Specific gravity compares the density of a substance with the density of a reference material.

In the case of gases, the reference material is standard dry air, or air without water. In the case of liquids and solids, the reference material is fresh water. Specific gravity is calculated by dividing the density of a substance by the reference substance's density.

For example, gold has a density of Water molecules are always moving. But on the average they are packed the same throughout.

## Physics Homepage

Therefore, the ratio between the mass and volume is the same, making the density the same. This is true no matter the size of the sample or where you select your sample from. Extend Have students consider whether the density of a large piece of a solid substance is the same as the density of a smaller piece. Give students time to calculate the density of each of the three samples drawn on their activity sheet and answer the related questions.

The density of a liquid is the same no matter what the size of the sample. Could this be true for solids, too? Calculate the density of each of the three samples to find out. The density of a solid substance is the same no matter how big or small the sample.

Sample A has a mass of g. What is the density of Sample A? What is the density of Sample B?

## Density of Water

If students do not know what the mass is, tell them that it is half the mass of Sample A. You then need to find the rise and the run between these two points. See the power point for further information. Finding the slope almost always tells us something about the variables. If the slope has a meaning in our class it always will we will then know that there is a relationship between the two variables and by calculating the slope we are able to write this relationship in form of an equation.

In math class this is done using the equation: In a lot of our examples this will be zero. Try to connect what you learned about slope in math to what we are doing in physics. When graphing mass and volume we do so to gain deeper insight into the relationship between these two variables. On a mass and volume graph for one type of material you will soon see that all points lie on one straight line. Think about what this means.

Not only are both variables proportional but the relationship between them is a fixed one.

The graph is linear. For every unit that you increase the mass, the volume increases by another fixed unit. In the graph at right three different materials are plooted amss against volume. You can see that for none of them the mass increses by the same unit as the volume does, although the red line which represents ice is close. Pay close attention to the axis, they are not the same. For the blue line, if the volume increases by one unit the mass increases by 8 units. That means that for every cubic cenitmeter that you increase the volume th amss goes up by 8g.

What does this number represent? If you think about this for a moment and remember what we talked about when we discussed proportional reasoning between mass and volume, it will be apparent that this is the density. The density can therefore be found by finding the slope on mass versus volume graph.

### Physics Homepage

If you flip the axi around you willl get the number that tels you by how much the volume increases if you increase the mass by one gram. This, although it has a meaning, does not have a name, as we discussed in class. If you flip the axis you will also note that now the red line will be the steepest. Here is a problem form the workbook that you might want to work through: Suppose we have a lump of clay represented by point P on the mass versus volume graph below.

Enough mystery metal is mixed with this lump of clay so that the resulting ball of clay and metal is represented by point Q. What is the density of pure clay without the metal? What is the density of the mystery metal?

I am sure you will have no difficulty in findg the density of the clay. Look at point P, divide the mass 15g by the volume 10 ccm. This will lead a density of 1.