Mass vs. Volume: Proportions and Density

If there is time, we highly recommend choosing some of the activities below. All of them can be considered science activities. Some of them seem like magic at first and the class will have a lot of fun watching and then explaining what they see. Activities can be done as teacher-led demonstrations, or student groups can be assigned different activities from the list to present to the class. They can explain why their “trick” isn't really magic, but just an application of density.

Margarine Tub Boats. Students can use their knowledge of mass, volume, and density to predict how much mass a boat can hold before sinking. One way to do this is to use margarine tubs as boats.

Students can determine the volume of the “boat” using a graduated cylinder and water. Since the walls of the margarine tub are relatively thin, the capacity, or inside volume, of the tub will provide a close estimate of the boat's total volume. (However, if you cut the tub into small strips, you can find its volume using a graduated cylinder and water. Adding the volume of the tub to its inside volume, or capacity, will give the total volume of the tub.)

Once students know the volume of the boat, they can apply what they learned in Sink and Float and Mass vs. Volume: Proportions and Density to predict the maximum amount of mass the boat can hold. They can test their prediction by first measuring the mass of the empty boat and then carefully filling the floating tub with standard masses until the boat sinks.

If the students made careful measurements, the total mass (in grams) of the empty boat plus the largest “load” of standard masses it can hold without sinking will be close to the volume of the boat in cubic centimeters. This would keep the density of the boat with its load approximately 1.0 g/cc, the density of water. (Note: Measurements that are within 10% should be considered reasonable.) This can be represented mathematically by the following equation:

See the discussion in Lesson Guide 3 of Questions 14 and 20 on the Sink and Float pages in the Student Guide. See the Content Note: Why Do Boats Float? in Lesson 3 as well.

Floating in Different Liquids: A Density Mystery. So far, students have considered sinking and floating only in water. What happens if you change the type of liquid? Liquids other than water are often messy to handle and can be expensive to buy for the entire class. For this reason, you might prefer to do a classroom demonstration.

1. Determine the density of vegetable oil and corn syrup. Since this is very messy, you might prefer to use the sample data (see Figure 5). The sample vegetable oil has a density of 0.9 g/cc and the corn syrup to has a density of 1.4 g/cc. (When finding the mass, don't forget to subtract the mass of the container.)
2. Ask students to add the mass vs. volume lines for these liquids to their graphs that show the sink and float pattern (see Figure 6). The line for syrup is above the line for water and the line for vegetable oil should be below. This means the corn syrup is denser and will sink in water and the vegetable oil is less dense and will float in water.
3. Have students predict what will happen when vegetable oil, water (with a few drops of food coloring added for a dramatic effect), and corn syrup are poured into the same container. (Ask them whether a liquid could float on another liquid.) Pour vegetable oil, then colored water, then corn syrup into a jar. The vegetable oil, although initially on the bottom, rises to the top. The corn syrup sinks to the bottom.
4. Ask students to predict which objects from the Sink and Float lesson will sink and which will float in each liquid. The patterns they used for water can be generalized to other liquids: an object floats in a liquid if its density is less than the density of the liquid. Equivalently, it floats if its mass-volume line is below the line for the liquid. Students should use their data or their graphs to make their predictions.
5. Drop the objects into the jar (if an object such as paraffin won't fit into the container, break off a small piece). Students will find, for example, that the plastic sphere that sinks in water now floats in syrup. Some crayons float in water but sink in vegetable oil.
6. You can ask students to continue this activity at home. Ask them to check for objects that float in water but not oil, in syrup but not water (a grape is an example of the latter), etc. Ask them to draw a picture of the liquids and objects as they appear in their jars. See Figure 7.

Mystery of the Floating Egg.

1. Put an uncooked egg in tap water. It sinks. See Figure 8.
2. Now remove the egg and dissolve salt in the water. It works well to use a ratio of about 20 cc of salt to 150 cc of water, or about 6 teaspoons of salt to 1 cup of water. Stir the salt into the water until it all dissolves completely.
3. Put the egg in the salt water. It floats. Why? Have you changed the mass or volume of the egg? No. Have you changed the volume of the water? Not much; when the salt dissolves in the water, the salt molecules fit in among the water molecules, so the volume of the mixture does not change much. But adding the salt does increase the mass of the solution. Adding salt increases the numerator in the density, M/V. Increasing the numerator gives a bigger ratio, hence a greater density. Salt water is denser than tap water. In fact it is a little denser than the egg. Thus, the egg floats.
4. You can make the lesson more quantitative by having the students measure the mass and volume of the egg and the salt water and compute the density of each. The density of our egg was 1.07 g/cc (we measured M = 60 g and V = 56 cc). With about 20 cc of salt per 150 cc of water, our salt water had a density of 1.08 g/cc. The density of our egg was less than the density of the salt water, so it floated.
5. During the demonstration, you can use the following discussion prompts.

Mystery of the Rising and Falling Raisin. Place a raisin (or several raisins) in a glass of clear soda. (Neither dried-out raisins nor diet soda work very well.) The raisin first sinks like a rock, then rises to the top, sinks again, and rises again for several up-down passages until it seems to get tired out and finally stays on the bottom. Why? Have students look closely at the raisin and ask them to figure it out using what they know about density.

Nothing happens to the liquid, so the density of the liquid does not change. Initially the density of the raisin must be greater than that of the liquid since the raisin sinks to the bottom. But then, the raisin picks up some of the gas that normally bubbles up in the soda. If students look closely, they can see the bubbles on the raisin. The added gas bubbles increase the volume of the raisin without increasing its mass, since each attached bubble has an infinitesimally small mass. This makes the density of the raisin-plus-gas less than the density of the water. The raisin with the added gas floats to the top. But when it gets to the top, the bubbles of carbon dioxide gas burst; the raisin returns to its original volume, and down it goes. The sequence is repeated several times until there is not enough gas left in the soda to “raise” the raisin. See Figure 9.