Mass, Volume and Density

Transcription

1 Mass, Volume and Density An integrated Science and Mathematics Exploration

2 Activity 1 Exploring Volume Materials: Set of 6 jars (labelled A-F) of same size A B C D E F Weighing scales Tape measure Ruler Pen and paper Calculator Water bath Cloth (for wiping up spills) Tea towel (for wiping jars) Large measuring jug (marked in ml) Activity 1 Worksheet 1. Without using the weighing scales, arrange the jars in order of heaviness by heft (lifting them and feeling how heavy they are). Write down the order. It is possible that your group will not agree on the order. 2. Using the weighing scales, find the mass of each container and reorder the jars. Record the mass of each jar. 3. Using the tape measure and/or ruler, make the following measurements of one of the jars (record these measurements on your page): Diameter of circle at base of jar: Radius of circle(diameter 2): Height of jar: 4. Calculate the volume of the jar and record it on your page. Volume means the amount of space something takes up. To find the volume of many 3D shapes, use the formula: area of base x height. The base of this jar is a circle 5. Find the volume of one of the jars by using the displacement method (record this measurement on your page): Put the jar into a measuring jug of water. Note the water level increase. 6. Discuss the following questions in your group (complete questions on your page): Did you get a similar result for volume using both the calculation and the displacement method? Should these two measures be the same? Why/why not? How would you describe the volume of each of the jars in the set? What can you say about the mass of each of the jars in the set? 7. Think about the meaning of the word density: Density is the relationship between the mass and volume of the object. All the jars in this activity have density (just as they also all have volume and mass). Density means considering both mass and volume at the same time. Which jar has the greatest density? Which jar has the least density? Why do you think so? The second activity is to assist you to do this.

3 Activity 2 Exploring Density Materials: Set of 5 jars (labelled 1-5) of different sizes Weighing scales Tape measure Ruler Pen and paper Calculator Water bath Cloth (for wiping up spills) Tea towel (for wiping jars) Large measuring jug (marked in ml) Activity 2 Worksheet 1. Order the jars from largest to smallest volume. 2. Discuss with your group whether you need to calculate volume to complete the first task and explain why or why not. 3. Without using the weighing scales, arrange the jars in order of heaviness by heft (lifting them and feeling how heavy they are). Write down the order. It is possible that your group will not agree on the order. 4. Using the weighing scales, find the mass of each container and reorder the jars. Record the mass of each jar. 5. Calculate the volume of each jar. Use the measuring tape or ruler to take appropriate measurements. Enter the information in the data table on the worksheet. 6. Find the volume of each of the jars by using the displacement method. Record the information in the data table on the worksheet. 7. Discuss the accuracy of your volume measurements using both methods. 8. Complete Data Table 2 on the worksheet. Calculate density by dividing mass by volume. 9. Discuss the following questions in your group: Which jar has the greatest density? How do you know? What do you need to consider when you are thinking about density? 10 By referring back to your calculations in Activity 1, complete Data Table 3 and calculate the density of jars A-F. 11. Refer to the data in Tables 2 and 3 and order the jars according to their density. 12. Discuss with your group the meaning of the word density. Write your definition of density on your worksheet.

4 Activity 3 Sinking and Floating Materials: Set of 6-8 jars of various volumes and masses. Weighing scales Tape measure Ruler Pen and paper Calculator Water bath Cloth (for wiping up spills) Tea towel (for wiping jars) Large measuring jug (marked in ml) Activity 3 Worksheet 1. Find the volume and mass of each of the jars and enter this information in the data table on the worksheet. Calculate the density of each jar. 2. For each jar, predict whether it will sink or float in water. Record your prediction in the data table on the worksheet. 3. Test whether your prediction was correct. Enter this information in the table on the worksheet. 4. Analyse the results of the data table. How can you predict whether something will sink or float in water? Write your reasoning on the worksheet. 5. Complete the questions on the worksheet.

5 Activity 1 Worksheet Exploring Volume Jar A B C D E Mass Diameter of Base: Radius of Base: Height: Area of Base: Volume of jar: (area of base x height) Volume by displacement: Questions: 1. What can you say about the volume of the jar using the calculation method compared to the displacement method? 2. Should the volume measure be the same using either of these methods? Explain. 3. Complete the following statement: Although the jars have the same, they all have a different. 4. Describe how to find volume by calculation: 5. Describe how to find volume by displacement: In this activity you explored the volume and mass of the jars. Another property that can be explored is the density of each jar. All the jars in this activity have density (just as they also all have volume and mass). Density is the relationship between the mass and volume of the object. Discuss: Which jar has the greatest density? Which jar has the least density? Why do you think so?

6 Activity 2 Worksheet Exploring Density Data Table 1 Volume and Mass of Jars 1-5 Jar Mass Diameter of base 1 Radius Area of base Height Volume (Area of base x height) Volume by displacement Data Table 2 Density of jars 1-5 Jar Mass Volume (approx) Density Mass/Volume Data Table 3 Density of jars A-F Jar Mass Volume (approx) Density Mass/Volume A B C D E PTO

7 List the jars in order of increasing density: Activity 2 Worksheet (Continued) Exploring Density Density: (Write your group s definition of density here)

8 Activity 3 Worksheet Sinking and Floating Data Table 1 Does it sink or float? Jar Mass Volume (approx) Density Mass/Volume Sink or Float? Prediction Sink or Float? Actual Questions 1. How can you predict whether something will sink or float in water? Refer to examples in your table to support your statement: 2. Jar X weighs 500g and has a volume of 400cm3. It sinks in water. Jar Y weighs 600 g and has a volume of 700 cm3. It floats on water. For each of the following jars, say whether they will sink or float in water and why you think so: a) Mass 500g, volume 300cm 3. sink float Reason: b) Mass 500g, volume 750cm 3. sink float Reason: c) Mass 250g, volume 200cm 3. sink float Reason: d) Mass 1500g, volume 1800cm 3. sink float Reason:

9 e) Mass 900g, volume 1200cm 3. sink float Reason: 3. A model ship weighs 3000 g. If it is to float, what can you say about its total volume? 4. I got a plastic submarine out of my cereal packet this morning. Sometimes it floats and sometimes it sinks. Its total volume is 5cm3. (a) What must its mass be to make it sink? (b) What must its mass be if it is to float? 5.a) What size will the bag of feathers be that would weigh the same as a brick? Explain. b) Will a kilogram of feathers weigh the same as a kilogram of bricks? Explain. c) Will a kilogram of feathers have the same density as a kilogram of feathers? Explain. d) Which has the greater density, a brick made out of clay or a brick the same size made out of foam? Explain.

10 Mass, Volume and Density An integrated Science and Mathematics Exploration 1. Exploring Volume 6 jars/cans with same volume but different mass Volume is measured in cubes. (a) (b) (c) (d) 100g 200g 400g 500g 800g 1000g In groups, students put the cans in order of heaviness (by heft). Students then use scales to measure the mass of each jar and alter the lineup of cans accordingly. Discussion: What can be said about the volume of these cans? (The volume of the cans is the amount of space that they take up. These cans all have the same volume.) What can be said about the mass of these cans? (The cans all have different mass.) How would you describe this set of cans? (That they all have the same volume but they have a different mass.) Introduce the word DENSITY. We can describe objects in terms of their density. Density is the relationship between the mass and volume of the object. These cans all have the same volume, so we may jump to conclusions by thinking that the heavier an object, the greater its density. We need to be able to consider both mass and volume at the same time. The second activity is to assist you to do this. Mathematically, the volume of these cans can by found by calculating the area of the base (which is a circle) and multiplying by the height. 2. Exploring mass and volume at the same time 5 jars/containers with different volumes but the same mass (a) (b) (c) 400g 400g 400g 400g 400g In groups, students put the cans into order from largest to smallest. Discuss: Are the cans ordered in terms of greatest to least volume? By heft, put the cans into order from heaviest to lightest. Volume is the amount of space taken up by an object

11 (c) (d) (e) (f) Using scales, weigh each can and alter the line-up according to heaviness. (all cans weigh the same, so the line-up should remain at greatest to least volume) Discuss: Which one of the cans has the greatest density? How do you know? What do you need to consider when you are thinking about density? See notes at end on Archimedes. Discuss other real situations: what size will the bag of feathers be that would weigh the same as a brick? Will a kilogram of feathers weigh the same as a kilogram of bricks? Will a kilogram of feathers have the same density as a kilogram of feathers? Which has the greater density, a brick made out of clay or a brick the same size made out of foam? 3. Exploring Density (a) Using the first set of 6 cans that all had the same volume, explore which cans float in water and those that sink. You will need a trough/bucket of water and a tray to catch the spillage. (b) Have students construct a table of results. The table below assumes that the cans all have a volume of 500 cubic centimetres. (c) Introduce the way density is written as a relationship between the mass and volume (for students in younger middle years grades, you may omit this column in the table). Table 1 Sinking and Floating Object Sink/Float? Mass Volume Density 1 F 100g 500cm 2 100/500 2 F 200g 500cm 2 200/500 3 F 400g 500cm 2 400/500 4 F 500g 500cm 2 500/500 5 S 800g 500cm 2 800/500 6 S 1000g 500cm /500 (d) Discuss the patterns that can be seen and ask students to discuss whether they can predict if an object will sink or float.

12 Density by Martha Marie Day, Ed.D. Sometime around 250 b.c., the Greek mathematician Archimedes was given the task of determining whether a craftsman had defrauded the King of Syracuse by replacing some of the gold in the King s crown with silver. Archimedes thought about the problem while relaxing in a bathing pool. As he entered the pool, he noticed that water spilled over the sides of the pool. Archimedes had a moment of epiphany. He realized that the amount of water that spilled was equal in volume to the space that his body occupied. This fact suddenly provided him with a method for differentiating a mixed silver and gold crown from a pure gold crown. Because a measure of silver occupies more space than an equivalent measure of gold, Archimedes placed the craftsman s crown and a pure gold crown of equivalent mass in two tubs of water. He found that more water spilled over the sides of the tub when the craftsman s crown was submerged. It turned out that the craftsman had been defrauding the King! Legend has it that Archimedes was so excited about his discovery that he ran naked through the streets of Sicily shouting "Eureka! Eureka!" (the Greek word for "I have found it!"). Archimedes had used the concept of density to expose the fraud. Density is a physical property of matter that describes the degree of compactness of a substance - in other words, how closely packed together the atoms of an element or molecules of a compound are. The more closely packed together the individual particles of a substance are, the more dense that substance is. Since different substances have different densities, density measurements are a useful means for identifying substances. For example, how could you distinguish a metric ton of feathers versus a metric ton of bricks if you could not see them? One metric ton of either feathers or bricks will have an identical mass of 1,000 kilograms (one metric ton). However, a metric ton of feathers will occupy a volume of almost 400 million cm 3 (about the size of four tractor trailer trucks), while a metric ton of bricks will occupy only one-half million cm 3 (about the size of a large-screen TV). The bricks are denser than the feathers because their mass is packed into a smaller volume. This relationship between the mass and volume of a substance is what defines the physical property of density:

13 Density = Mass/Volume Density is an intensive property of matter that is defined as the ratio of an object's mass to its volume. Mass is the amount of matter contained in an object and is commonly measured in units of grams (g). Volume is the amount of space taken up by a quantity of matter and is commonly expressed in cubic centimeters (cm 3 ) or in milliliters (ml) (1cm 3 = 1 ml). Therefore, common units used to express density are grams per milliliters (g/ml) and grams per cubic centimeter (g/cm 3 ). Let's look at an example. A typical brick has a mass of 2,268 g and occupies a volume of 1,230 cm 3. The density of the brick is therefore: 2,268 g/1,230 cm 3 = 1.84 g/cm 3 Density is an easy concept to confuse. For example, many items that we commonly think of as "light" or "heavy" do not have different masses, but they do have different densities. Look at the table below for examples of the densities of common substances. Density of Some Common Substances Substance Density (g/cm 3 ) Air Feathers Wood(Oak) Ice 0.92 Water 1.00 Buoyancy Bricks 1.84 Aluminum 2.70 Steel 7.80 Silver Gold When Archimedes stepped into his bathing pool, not only did he realize that water spilled over the edges, but he also noticed something that we all notice when we go swimming - he felt lighter. The ability of an object to "float" when it is placed in a

14 fluid is called buoyant force, and is related to density. If an object is less dense than the fluid in which it is placed, it will "float" on the fluid. If it is more dense than the fluid, it will "sink." This concept explains why some objects float on water while others sink. For example, wood floats on water because it is less dense; steel by comparison sinks because it is denser than water. How, then, can large steel cruise ships stay afloat? Large ships have a tremendous amount of space in them that is filled with air (think about it: cabins, movie theaters, onboard casinos, etc.). While steel is denser than water, air is less dense. Metal ships can float because their total density is less than that of the water that they float on. When the metal hull of a ship is breached, like when the Titanic struck an iceberg, water rushes in and replaces the air in the ship s hull. As a result, the total density of the ship changes and causes the ship to sink. This concept of changing density is commonly employed in another type of ship, a submarine. A submarine has a constant volume but it can vary its mass by taking in water into its ballast tanks. When water is taken in to the ballast tanks, the mass (and thus density) of the submarine increases and the submarine attains negative buoyancy that allows it to submerge into the ocean depths. Conversely, when water is released from the ballast tanks the vessel s density decreases allowing it to surface. The concept of density also explains another common phenomenon. Have you ever noticed what happens to a bottle of oil and vinegar salad dressing when it is allowed to sit still after it has been shaken? The oil will rise to the top and the vinegar will settle to the bottom of the bottle. This happens because oil is less dense than vinegar. When materials of different densities are put in contact with one another, their densities will determine how they order themselves. This phenomenon, where materials layer themselves according to their density, is called superposition. Another factor that can affect the density of a material is temperature. Many materials expand when they are heated. Because a material that expands will take up a larger volume, its density will decrease. This fact most commonly occurs with gases and some liquids and explains how hot air balloons work. When the air inside of a balloon is heated it expands and its density decreases. The balloon thus gains positive buoyancy with respect to the colder air surrounding it and it floats into the sky. Density is an important physical property of matter. It is commonly used as a means of categorizing and identifying different materials. In addition, a thorough understanding of the concept of density is critical for building ships and lighterthan-air craft such as hot air balloons. Source: Accessed 13 March 2007.

15 Exploring the Balance Beam Boat Materials: 30cm wooden ruler, drawing pin, 10cm x 6cm cork sanding block, plasticine, plastic tote tray, water 1. Find the mid-point of the ruler and mark with a water-proof pen. 2. From the mid-point of the ruler, mark 4 evenly-spaced sections on either side of the ruler. Number as per the diagram below Find the mid-point of the sanding block and mark. 4. Insert a drawing pin into the ruler at the mid-point and insert that through the mid-point of the sanding block. You might have to adjust the position of the drawing pin to ensure that the ruler is in balance. 5. Test that your boat and ruler is in balance by placing it in the tub of water. 6. Cut each stick of plasticine into 4 evenly-sized pieces. 7. Experiment with various numbers of plasticine weights and positions on the ruler by undertaking the tasks below. Task 1 Place one weight on the four (4) position on one side of the ruler. Test all the possible ways of balancing this weight. Record your findings by making drawings of what you have found. 1

16 Task 2 Task 3 2

17 Task 4 Task 5 3

18 Creating a Data Set 4

19 MORE BALANCING IDEAS The same volume of water is poured into each of these containers. The surface area and depth of water in each container is listed in the table. Container Surface Area Depth 1 100cm 2 5cm 2 50cm 2 10cm 3 20cm 2 25cm 4 10cm 2 If the same amount of liquid was poured into container 4, its surface area is 10cm 2. How deep is it? Record your answer in the table. In your own words, describe what happens to the depth of the liquid if you change the surface area. How can you accurately calculate the surface area if told the volume and depth of the liquid? How can you accurately calculate the depth of the liquid if told the volume and surface area? How can you accurately calculate the volume of the liquid if told the surface area and depth of container? 1

20 Life as a Pond Plant A pond plant will produce bubbles of oxygen in water when a bright light is shone on it. The pictures show how many bubbles are given off in ten minutes when a lamp is put at different distances from the plant. Measure the distance of each plant from the light. Enter this information in the first column of the table below. Count the number of bubbles in each test tube. Record this in the third column. Plant Number 1 Distance from light Distance Squared Number of bubbles Bubbles x Distance Squared 2 3 The light reaching the plant gets less, proportionally, to the square of the distance of the lamp. This means that if you double the distance of the lamp, you reduce the amount of light to one quarter of its amount. Complete columns 2 and 4 by performing the calculations listed. Study your completed data table. What do you notice? What is the relation between the amount of light that falls on the plant and the number of bubbles of oxygen that are given off? If you were to use a dimmer lamp, what could you do to make it produce the same amount of oxygen? 2