Density
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This document discusses density and how it relates to whether objects float or sink. It defines density as mass divided by volume, meaning the amount of matter contained in a certain space. Objects with higher densities are more compact and have more mass for their volume. The document explains that while a kilogram of rocks and feathers have the same mass, the rocks have a higher density and are therefore heavier. It concludes that boats float because they are less dense than water, while paperclips sink due to their higher density.
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Density
- 1. DENSITY
- 2. Do Now What is heavier, a kilogram of rocks or a kilogram of feathers? Why do you think so? Write your answer in your student worksheet
- 3. Paper clip What happens when you drop a paper clip in a cup of water?
- 4. Why does a cargo ship float while the tiny paperclip sinks?
- 5. Defining Mass and Volume MASS: VOLUME: a measure of the amount of matter in an object The quantity of three-dimensional space an object occupies How do we measure it? A balance or scale How do we measure it? Multiplying dimensions or displacement method
- 6. Density Density = Mass Volume The mass per unit volume in an object How much matter there is in a given amount of space
- 7. How are these the same and different? Similarities DifferencesDifferences Rubber ballStyrofoam ball
- 8. 1. Use a scale to measure the mass of each ball How are these the same and different? Volume sphere = Π r3 4__ 3 Density = __________ Volume Mass 2. Calculate the volume of each ball using 3. Calculate the density of each sphere using
- 9. Density – Same Volume, Different Mass If two objects have the same volume but one has a greater mass, the object with a greater mass has a higher density.
- 10. How are these the same and different?
- 11. Density – Same Mass, Different Volume If two objects have the same mass but one has a smaller volume, the object with smaller volume has a higher density.
- 12. So why does the boat float while the paper clip sinks?
- 13. Wrap Up What is heavier, a kilogram of rocks or a kilogram of feathers? Why do you think so? 1 kg 1 kg
Editor's Notes
- #6: Show this after the class has come up with their own definitions
- #7: Denser things feel heavier, less dense things feel lighter. But don’t confuse density with weight or mass – IT ALSO DEPENDS ON THE VOLUME.
- #8: Students will first carry out a qualitative comparison of the balls, describing characteristics they can see but cannot measure numerically. Ask students to follow the following directions: 1) As a team, compare and contrast the Styrofoam and rubber balls, discussing the differences and similarities between them. 2) Organize your ideas from step 1 into the double-bubble thinking map in your student worksheet: the properties the balls have in common should go in the center boxes, while the properties unique to each ball should go on the boxes to the left and the right. Debrief: As a class, discuss the students findings. Students should note that although the balls have the same volume, they have different masses.
- #9: Refer back to the density formula and ask students whether they think that the balls’ densities will be the same or not. Explain that to answer that question, they will complete a quantitative comparison—one involving characteristics that can be measured numerically. 1) Measure the mass of each ball using a scale. Record your measurements in the student worksheet. 2) Measure the volume of the balls using the following formula (see Calculating Volume of a Sphere handout for step-by step instructions): 3) Use the measured masses and volumes to calculate the density of each ball using the density formula (Density = Mass/Volume)
- #11: 1. Gather the class together and show them the steel spheres from the Steel Sphere Density Kit. 2. Ask students to compare and contrast the qualitative characteristics of the spheres. They will note the similar shape, color, material, and reflective surface. They will also immediately notice the difference in volume. 3. Ask for a volunteer to come up to the front and hold one of the steel spheres in each hand. Do the spheres weigh the same? Do they have the same mass? The student will likely say that the smaller sphere weighs more (has more mass). Tell the students that the mass of the spheres is very close to the same (large sphere = 123 g; small sphere = 115 g), even though the volume of the spheres is quite different. 4. As a class or in small groups, calculate the volume of each sphere. (large sphere diameter = 12.7 cm; small sphere diameter = 3.49 cm). The volume of the large sphere is 1,069 cm3, and that for the small sphere is 22 cm3. 5. Using the masses from step 4 and the volume from step 5, calculate the density of each sphere.
- #12: 6. As a class, discuss the students’ findings. Students should note that if two objects have the same mass but one has a smaller volume, the object with the smaller volume has a higher density. 7. Ask the students to think back to the cargo ship and the paperclip. As they do, place the 2 spheres in water and show students how the lower density sphere floats, while the higher density one sinks.
- #13: Why does a heavy cargo ship float while a tiny paperclip sinks? It’s all about density! While the total mass of the ship is very large, the average density of a ship -- the combination of the steel and the air -- is very small compared to the average density of water. Conversely, the average density of the paper clip is greater than 1 g/cm3, so even though its mass is miniscule compared to the ship’s, it sinks in the glass of water.
- #14: Same mass Different volume Which is denser?