ACTIVITY 1: Density--KEY

Transcription

1 CYCLE 5 Developing Ideas ACTIVITY 1: Density--KEY Purpose Just as you have various traits, materials have traits, or properties. Some of your traits are similar to the traits of others one heart, two lungs, one brain. Some of your traits are different from the traits of others, and therefore, distinguish you from others your height, body shape, facial features, vocal patterns, etc. Likewise, some properties of different materials may be similar, but others may be different, and therefore distinguish one material from another. The first property of materials that you will investigate is density. You may have encountered the idea of density in many different contexts: dense crowds, high density disks for computers, low density housing in the suburbs. The property of density is related to these other contexts, but has a more precise definition which you will develop in this activity. Also, it is difficult to measure the density of a material directly. Therefore it is important for us to determine which other properties of a material allow us to determine its density. In this activity you will investigate the density of different materials, and the relationship between density and other properties of a material. What physical properties of a material contribute to its density? Initial Ideas Consider the following scenario and answer the questions. You have two rings that look the same. One ring is made of solid gold while the other is only gold plated. You keep the solid gold ring in a special bag when you are not wearing it, but you keep the gold-plated ring in your jewelry box. One day, you open your jewelry box to discover that you have accidentally placed both rings inside. Neither ring has distinguishing markings with which to tell them apart PSET 5-1

2 Cycle 5 What property(s) of the rings might be helpful in determining which one is made of solid gold? Possible student answers: heaviness, how much they weigh, the solid gold ring will be softer, the gold-plated ring might turn your finger green when you wear it, I just don t know how to tell them apart. Share your ideas with other members of your group and listen to them as they describe their ideas about these situations. Participate in a whole class discussion. Be prepared to share your ideas with the rest of the class. Collecting and Interpreting Evidence Experiment #1: How are mass and volume different? You will need: 2 blocks with the same dimensions, each one made of a different material from the list: acrylic, aluminum, brass, copper, oak, pine, polypropylene, PVC, steel Electronic balance In this experiment you will compare the mass of two blocks that have the same dimensions, and hence, the same volume, but are made of different materials. STEP 1. Record the material that makes up each block in the following data table. Table 1: Mass of Blocks with Same Volume Material Block 1 Block 2 Mass g g 5-2 STEP 2. Use a balance to obtain the mass of each block in grams (g). Record your measurement in the data table above.

3 Activity 1: Density Do equal volumes of different materials have the same mass? If not, which material had the greater mass per unit volume? How did you figure this out from the data table? No, equal volumes of different materials do not have the same mass. Since the blocks have the same volume, the one with the greater mass has the greater mass for the same volume. In principle, this would be true for any volume, so we can refer to a unit volume (a volume with a unit value for volume, for example, 1 cm 3.) Therefore, the greater mass has the greater mass per unit volume. You will need: 2 blocks of about the same mass, each one made of a different material from the list: acrylic, aluminum, brass, copper, oak, pine, polypropylene, PVC, steel Metric ruler Calculator In this experiment you will measure the dimensions of blocks having the same mass but made of different materials. You will use these measurements to calculate the volume of each block. STEP 3. Record the material that makes up each block in the following data table. Follow the instructions given in Steps 4 and 5 for completing the rest of the table. Table 2: Volume of Blocks with Same Mass Block 1 Block 2 Material Length cm cm Width cm cm Height cm cm Volume cm 3 cm 3 STEP 4. Use a ruler to measure the length, width and height of each block in centimeters (cm). Record your measurements in the data table above. 5-3

4 Cycle 5 STEP 5. Calculate the volume of each block using the relationship: Volume = (length) x (width) x (height) Record the volume in cubic centimeters (cm 3 ) in the data table above. Do equal masses of different materials have the same volume? If not, which material had the greater volume per unit mass? How did you figure this out from the data table? No, equal masses of different materials do not have the same volume. Since the blocks have the same mass, the one with the greater volume has the greater volume for the same mass. In principle, this would be true for any mass, so we can refer to a unit mass (for example, 1 gram Therefore, the greater volume has the greater volume per unit mass. How is mass different from volume? What does each measure? Volume measures the amount of space that an object occupies. Mass measures how much material is actually in the object. When we refer to the amount of a material, generally we are referring to the mass, not the volume. (Students may suggest mass is weight, rather than mass being proportional to weight. In Cycle 3 they learned that the more mass an object has, the greater is the gravitational force on it due to the earth. The gravitational force is the weight.) Measuring Mass and Volume Accurately When scientists perform an experiment to measure a quantity, they never obtain an exact value. There is always some uncertainty associated with a measurement. The goal of making good measurements is to reduce the amount of uncertainty. How carefully the measurement is taken, the precision of the measuring instrument, and how many times the measurement is taken all affect the uncertainty of the value. Therefore scientists always report a best value, not an exact value for the measurement. Knowing the uncertainty of a measurement allows scientists to compare two values to know if they are the same or different. Mass is a physical property of all materials that is related to the amount of material. Mass is usually measured in units of grams or kilograms using balances. The mass of an unknown object can be measured by putting it on one side of an equal arm 5-4

5 Activity 1: Density balance and adding known masses to the other side of the balance until the masses are balanced. Typically, these known masses are unit masses, objects that have a mass of 1 gram. In this way we can define the mass of an object as the number of unit masses that balance the object. Today mass is commonly measured using electronic balances. The measurements of mass obtained using balances are only as exact as the known masses and the ability of the balance to measure mass precisely. Since most electronic balances measure mass to the nearest 0.1 (tenth) or 0.01 (hundredth) of a gram, the uncertainty of mass measurements is typically ±0.05 or grams. For most of the mass measurements you will be taking, this uncertainty is much smaller than the mass you are trying to measure, so we will usually ignore the uncertainty when reporting mass measurements. Volume is a physical property of all materials that is related to the amount of space a material occupies. For objects whose corners are all at right angles, volume is usually measured by using a ruler to measure the length, width and height of the object in centimeters. The volume is then calculated as follows: Volume = (length) x (width) x (height), and is measured in units of cubic centimeters (cm 3 ). As these units suggest, the volume of an unknown object can be measured by counting the number of unit cubes, cubes with a volume of 1 cm 3, that it takes to fill the object. For irregularly shaped objects, it is difficult to calculate the volume by measuring the object s dimensions, so their volume is commonly measured by liquid displacement. In this method, the initial volume of a liquid, usually water, in a graduated cylinder is measured. Then the object is placed in the water and a final volume is measured. The volume of the object is the difference of the initial and final volumes of the water and is usually measured in milliliters (ml). Since the volume contained in a 1 cm 3 cube is equal to 1 ml when poured into a graduated cylinder, the units of ml and cm 3 are often used interchangeably. 5-5

6 Cycle 5 The measurements obtained using rulers and graduated cylinders are only as exact as the scale on the ruler or the graduated cylinder. Since most rulers have a scale to the nearest 0.1 (tenth) of a centimeter, the uncertainty of length measurements is typically ±0.05 centimeters. The uncertainty in the volume is a function of the uncertainties of each of the dimensions. Similarly, many graduated cylinders have a scale to the nearest 1 ml, as you can see in the picture above, so that the uncertainty in volume is typically ±0.5 ml. For most of the volume measurements you will be taking, this uncertainty is much smaller than the volume you are trying to measure, so we will usually ignore the uncertainty when reporting volume measurements. Experiment #2: Is there a relationship between the mass and volume of a material? You will need: 3 objects of different sizes/shapes, each one made of the same material from the list: acrylic, aluminum, brass, copper, oak, pine, polypropylene, PVC, steel; preferably one of the objects should be a unit cube with a volume of 1 cm 3, and one should irregularly shaped Electronic balance Metric ruler Graduated cylinder Water Calculator STEP 1. Record the material that you chose in Table 3. Follow the instructions given in Steps 2-9 for completing the rest of the table. Table 3: Masses and Volumes for Objects of the Same Material 5-6

7 Activity 1: Density Object 1 Object 2 Object 3 Material: Mass g g g Length cm cm cm Width cm cm cm Height cm cm cm Volume (ruler) cm 3 cm 3 cm 3 Initial Water Volume ml ml ml Final Water Volume ml ml ml Volume (displacement) ml (cm 3 ) ml (cm 3 ) ml (cm 3 ) Ratio mass/volume g/cm 3 g/cm 3 g/cm 3 STEP 2. Use a balance to obtain the mass of each object in grams (g). Record your measurement in the data table. STEP 3. For regularly-shaped objects, you can calculate the volume of the object. Measure the length, width and height in centimeters (cm) of any square- or rectangular-shaped objects. Record your measurements in the data table. STEP 4. Calculate the volume of those objects using the relationship: Volume = (length) x (width) x (height) Record your result in cubic centimeters (cm 3 ) in the data table. STEP 5. For irregularly-shaped objects, you must measure the volume of the object using liquid displacement. Fill the graduated cylinder halfway with water. Measure the volume of water in the cylinder by moving your head so that your eye is at the same level as the water level. The water in the cylinder curves up at the edges, forming what is called a meniscus. Read the volume of the water in milliliters (ml) by observing which line the bottom of the curve crosses. Record this measurement as the initial water volume in the data table. 5-7

8 Cycle 5 STEP 6. Carefully drop the irregularly-shaped object into the graduated cylinder and measure the resulting volume of the water as in Step 5. Record your measurement as the final water volume in the data table above. STEP 7. Calculate the volume of the object using the relationship: Volume = (final water volume) (initial water volume) Record your result in milliliters (ml), which are equal to cubic centimeters (cm 3 ), in the data table above. STEP 8. If possible, determine the volume of one regularly-shaped object by calculating from length, width, and height, and by liquid displacement. How do the volumes you measured for the same object by two different methods compare? Why might the measured volumes be different? The volumes obtained by measurement and by liquid displacement should be fairly close. They may be different due to uncertainty of the measuring devices (estimation between calibration lines) or due to measurement errors (using the top of the meniscus instead of the bottom, etc.) STEP 9. Calculate the ratio of the mass of each object to its volume using the following relationship: Ratio = (mass) / (volume) Record your result in grams per cubic centimeter (g/cm 3 ) in the data table. How do the masses for different objects of the same material compare? The masses are different for different objects of the same material (assuming different volumes) How do the volumes for different objects of the same material compare? The volumes are different for different objects of the same material (assuming different masses) 5-8 How does the ratio of mass/volume compare for different objects of the same material? The ratios of mass/volume are fairly close for different objects of the same material.

9 Activity 1: Density Are these ratios the same? How close do the values need to be for you to consider them as the same value? Why might the values be different? Within experimental uncertainty, these ratios can be considered to be the same. The variation occurs from uncertainty in measurement, or may be the result of measurement errors. Characteristic Properties and Density Properties of materials that can be observed or measured without changing the composition of the material are called physical properties. Some physical properties allow us to identify materials. These physical properties that are specific to a material and can be used to distinguish one material from another are called characteristic physical properties. As you have observed, each object has a mass and a volume. Mass and volume are physical properties. An object s mass indicates the amount of material in an object (e.g. the number of 1 g unit masses that balance the material on an equal arm balance) while its volume indicates how much space an object occupies (e.g. the number of 1 cm 3 cubes that fit inside the object). Since different objects of the same material can have different masses and different volumes, mass and volume are not enough to identify a material. However, as you discovered, the ratio between an object s mass and volume is the same for all objects of the same material. This ratio can help you identify what material an object is made of, and is therefore, a characteristic physical property of a material. The ratio of mass/volume is defined as the density of the material and is equal to the amount of mass occupying one unit of volume. In other words, the density of a material gives us the mass of a 1 cm 3 unit cube of a material. We calculate density using the relationship: Density = (mass) / (volume) A table of densities for various materials is given below. Share your calculated densities with other groups who studied different materials, and record the calculated values in the table. Compare your calculated densities to the values in the table. Table 4: Densities and Calculated Values 5-9

10 Cycle 5 Material Density (g/cm 3 ) Acrylic 1.4 Aluminum 2.7 Brass 8.5 Copper 8.9 Oak 0.7 Pine 0.5 Polypropylene 0.9 PVC 1.3 Steel 7.8 Calculated Value How do your calculated densities compare? Why might your values be different from those in the table? Values are usually fairly close; precision of measuring instruments used, human error estimation is different for different people, consistency we didn t always use the same instruments or have the same person determining the measurement value in the case of volume. Experiment #3: How do the densities of liquids and gases compare to the densities of solids? Water Electronic balance 10- or 25-mL graduated cylinder Balloon Metric ruler String Calculator STEP 1. Measure the mass of the empty graduated cylinder. Record the measurement in Table 5 as the mass of beaker. Follow the instructions given in Steps 2-5 for completing the rest of the table. Table 5. Density of Water 5-10

11 Activity 1: Density Mass of beaker g Mass of beaker + water g Mass of water g Volume of water ml (cm 3 ) Density of water g/cm 3 STEP 2. Accurately measure approximately 10 ml of water in the graduated cylinder. Record the measurement in Table 5 as volume of water. STEP 3. Measure the mass of the graduated cylinder and water. Record the measurement in Table 5 as mass of beaker + water. STEP 4. Calculate the mass of the water sample using the relationship: Mass of water = (mass of beaker + water) (mass of beaker) Record this value in Table 5. STEP 5. Calculate the density of water using the relationship: Density = (mass) / (volume) Record this value in Table 5. Which solids from Experiment #2 have densities less than water? Which have densities greater than water? Water has a density of 1.0 g/cm 3. Oak, pine, and polypropylene have densities less than water. Acrylic, aluminum, brass, copper, PVC, and steel have densities greater than water. If you are using sensitive electronic balances, you should perform the next experiment. Otherwise, your instructor will show you a video of an experiment being performed. In this experiment, the mass and approximate volume of breath will be measured in order to estimate the density of breath. Breath is a mixture of gases, primarily nitrogen, oxygen, carbon dioxide, and water. STEP 6. Squeeze as much air out of the balloon as possible. Measure the mass of the empty balloon. Record the measurement in Table 6 as the mass of balloon. Follow the instructions given in Steps 7-12 for completing the rest of the table. 5-11

12 Cycle 5 Table 6. Density of Breath Mass of balloon 2.7 g Mass of balloon + breath 15.2 g Mass of breath 12.5 g diameter of balloon 27 cm Volume of breath 10,305 ml (cm 3 ) Density of breath g/cm 3 STEP 7. Inflate the balloon using your own breath. Tie the balloon off to keep air from escaping. STEP 8. Measure the mass of the breath-filled balloon. You may wish run a piece of string under the balance and around the balloon to hold it in place without adding extra mass to the measurement. Record the measurement in Table 6 as the mass of balloon + breath. STEP 9. Calculate the mass of the breath inside the balloon using the relationship: Mass of breath = (mass of balloon + breath) (mass of balloon) Record this value in Table 6. If you know the diameter of anything that has the shape of a sphere you can calculate its volume according to the relationship: Volume of sphere = (4/3) x (π) x (d/2) 3 Most balloons are not perfect spheres. However, we can obtain a good approximation for its volume and use it to estimate the density of breath. STEP 10. Using the string, measure the diameter of the breath-filled balloon. Record the measurement in Table

13 Activity 1: Density What other method for determining volume would give a more accurate value in this case? Because a balloon is not a perfect sphere, our calculation was only an approximation. A method for determining an accurate volume of this irregularly shaped object would be liquid displacement, but we would have to be sure the entire balloon was submerged under the water (and we d need to take into account the volume of the device used to hold the balloon under water, like the tip of our fingers). STEP 11. Assuming that all of the balloon s volume came from your breath, calculate the volume of breath using the relationship given for the volume of the sphere. Record the value in Table 6. STEP 12. Calculate the density of breath using the relationship: Record this value in Table 6. Density = (mass) / (volume) 5-13

14 Cycle 5 Table 7 lists the densities of some other liquids and gases. Table 7: Densities of Some Liquids and Gases Liquid Density (g/cm 3 ) Gas (at 20 C and 1 atm pressure) Vegetable oil 0.93 Air Gasoline 0.73 Hydrogen Ethyl Alcohol 0.79 Helium Liquid Hydrogen Chlorine Density (g/cm 3 ) In general, how do the densities of gases compare to those of liquids and solids are gas densities significantly greater, similar, or significantly less? Gas densities are significantly less than densities of liquids and solids. In the table above, vegetable oil is more than 10,000 x greater than the density of hydrogen gas! Summarizing Questions Discuss these questions with your group and note your ideas. Leave space to add any different ideas that may emerge when the whole class discusses their thinking. S1. Why are mass and volume not considered characteristic physical properties, but density (which is calculated from mass and volume) is? Different samples of the same material can have different masses and volumes. But different samples of the same material will always have the same density (the ratio of mass to volume). Density can be used to identify samples made from this material. 5-14

15 Activity 1: Density S2. Consider the conversation between two students about why the water level rises when a person sits down in a bathtub filled with water. I think that the water level rises in the bathtub because of mass. I think a 70 kg person will displace the same amount of water as any object with the same mass, even if the object takes up a lot less space than the person. I disagree. The water level rises in the bathtub because of volume the space that a person occupies. If a 0.1 m 3 person is submerged, then 0.1 m 3 of water will be displaced, no matter what mass the person has. Kristin Daryl Imagine that you were a third member of their group. Describe a simple experiment (using only a graduated cylinder, an electronic balance, and a few blocks) that would provide evidence to contradict one idea and support the other. What would you expect to observe in your simple experiment? Experiment #1: Use two blocks made of different materials that have the same mass they will have different volumes. When dropped in a graduated cylinder filled with water, the blocks will displace different volumes of water. This experimental evidence contradicts Kristin s ideas. Experiment #2: Use a third block made of a different material that has a volume equal to that of one of the other two blocks these two blocks will have different masses. When dropped in a graduated cylinder filled with water, the blocks will displace equal volumes of water. This experimental evidence supports Daryl s ideas. 5-15