Includes Teacher's Notes and Typical Experiment Results Instruction Manual and Experiment Guide for the PASCO scientific Model SE-9719 012-07192A 07/99 DISCOVER DENSITY SET © 1999 PASCO scientific $7.
Discover Density Set 012–07192A
012–07192A Discover Density Set Table of Contents Section Page Copyright, Warranty, and Equipment Return ............................................................................... ii Introduction ................................................................................................................................ 1 Equipment ................................................................................................................................. 2 Actitivies .......................
Discover Density Set 012-07192A Copyright, Warranty, and Equipment Return Please—Feel free to duplicate this manual subject to the copyright restrictions below. Copyright Notice The PASCO scientific 012-07192A Discover Density manual is copyrighted and all rights reserved. However, permission is granted to nonprofit educational institutions for reproduction of any part of the manual providing the reproductions are used only for their laboratories and are not sold for profit.
012–07192A Introduction Discover Density Set The PASCO SE-9719 Discover Density Set provides materials and activities to guide students through some basic graphical analysis techniques. In each case, an example is worked out, with explanations, and then the student is asked to perform a similar analysis based on the materials in the set. In the first analysis, students discover the concept as a mathematical constant relating measurements of a particular substance.
Discover Density Set Equipment 012–07192A Included: • PASCO SE-9719 Discover Density Set Figure 1 Contents of the SE-9719 Discover Density Set 2
012–07192A Discover Density Set Activities The Speed of Sound (pre-lab) Introduction This sample problem presents you with experimental data, and then leads you through a process to obtain an equation that relates the data. A similar problem based on the materials in this set is left for you to do, based on the same process. The method is then extended to more complex situations. A lightning bolt struck the earth, and upon seeing it, a number of observers started timing, using stopwatches.
Discover Density Set 012–07192A In algebra, the formula for a graph such as above is often given by: y = m x + b, where y is the variable on the vertical axis, x is the variable on the horizontal axis, b is the point on the vertical axis where the line intersects, and m is the slope of the line. The slope is found by marking two points on the line, and dividing the difference in y-coordinates (called the rise) by the difference in x-coordinates (the run).
012–07192A Finding an Equation Relating Mass and Volume Discover Density Set Introduction In this activity you are given four rectangular solid metal pieces, and four similar plastic pieces. You are asked to take data, organize it, graph it, and create equations relating the mass and volume of each of the two kinds of material. A minimum of instructions are given. You should study and follow the example titled “The Speed of Sound” which preceded this task.
Discover Density Set 012–07192A 8. Write equations for each of the two lines obtained. Use meaningful symbols, such as “m” and “v”. Include dimensional units in the constant. 9. Find the mass, volume, and density of the transparent rectangular solid and the black rectangular solid from compartments C1 and C2. Plot them on the same graph as the aluminum and PVC.
012–07192A The Mass of Fluorite Octahedra (Pre-lab) Discover Density Set Introduction Developing a mathematical equation from a set of experimental data is an extremely useful skill. The examples that follow show a method that will work for a great many physics phenomena. Then you will be asked to apply the method to data in a lab situation. The mineral fluorite is often found in geometric shapes having eight faces which are equilateral triangles.
Discover Density Set 012–07192A We might guess, for the fluorite example, that the exponent is 2, so y = c x2. This could be expressed in words as “y is proportional to x2.” Making a new table results in the following: (A computer spreadsheet program is an efficient way of creating such tables.) x2 edge2 (cm2) 0.6 1.7 4.0 7.3 13.7 y mass (g) 0.8 3.3 12.0 29.5 75.9 A graph of the above data does not result in a straight-line, as would have been the case if y had been proportional to x2. See Figure 3.
012–07192A Discover Density Set The corresponding graph from table of x3 and y values is straight, and thus shows that y is proportional to x3. See Figure 4. x3 edge3 (cm3) 0.5 2.2 8.0 19.7 50.7 y mass (g) 0.8 3.3 12.0 29.5 75.9 Figure 4 Graph of x3 vs mass The analysis has established that y = c x3. The constant of proportionality, c, is simply the slope of the graph.
Discover Density Set 012–07192A The final equation is thus: y = 1.47 g/cm3 x3, and replacing the symbols x and y with more meaningful symbols (e for edge, m for mass), the final result is: m = 1.47 g/cm3 e3. Although this is sometimes a tedious way to discover an equation representing data, a graph such as that in Figure 4 is a common and effective way to visually show the relationship.
012–07192A Discover Density Set Figure 5 Graph of the log transformation of the experimental data The straight-line graph (Figure 5) is confirmation that y = c xk was indeed the form of the equation. The slope of this graph is 3, showing that the exponent k is 3. The constant c may be evaluated by various methods. Perhaps the best is by solving the equation for c, and substituting data from the original table. Given that y = c x3 , c = y / x3 , and substituting x = 2.7 cm, y = 29.
Discover Density Set 012–07192A As an alternative to calculating the logarithms of all of the data, the data may be plotted on log-log graph paper, also called full logarithmic paper. The spacing between the lines on this paper is adjusted so that the appearance is the same as plotting the logarithms of the data on ordinary paper. The result is a straight line with a slope of 3.
012–07192A Finding an Equation Relating Mass and Diameter of Transparent Plastic Spheres Figure 6 Using the rectangular solids to increase the accuracy of the measurement of the diameter of a cylinder Discover Density Set Introduction In this activity you are given four transparent plastic spheres of different diameters. You are asked to take data, organize it, graph it, and create an equation relating the mass and diameter of the spheres. A minimum of instructions are given.
Discover Density Set 012–07192A Your instructor may tell you which method(s) to use. 6. Check the accuracy of the equation by using the following data from published sources: volume of a sphere = (4/3)π r3 radius = diameter / 2 density of the sphere material = 1.18 g/cm3 density = mass / volume 7. Algebraically combine this information to produce an equation giving the mass of these spheres in terms of their diameter. 8. Compare this result with the equation you determined experimentally.
012–07192A Discover Density Set and height. Since it is difficult to analyze data from experiments in which more than two variables, you group the cones into two groups. One group all have the same height, and the other group all have the same diameter. Two others did not fit in either group. Measuring the cones gives the following results: Group One are all 2.0 cm in diameter Height Mass 3.0 cm 5.56 g 4.0 cm 7.41 g 5.0 cm 9.27 g 6.0 cm 11.12 g Group Two are all 2.0 cm tall Diameter Mass 2.0 cm 3.71 g 3.
Discover Density Set 012–07192A The result of such an analysis is the discovery that y is proportional to x2. In other words, mass is proportional to diameter2. Evaluating the constant c is not needed. An Important Theorem: If a quantity is proportional to a second quantity, and the first quantity is also proportional to a third quantity, then the first quantity is proportional to the product of the second and third quantities. Applying this theorem to the example at hand makes this concept more clear.
012–07192A Finding an Equation Relating Mass to Length and Diameter of Black Plastic Cylinders Figure 7 Using the rectangular solids to increase the accuracy of the measurement of the diameter of a cylinder Discover Density Set Introduction In this activity you are given eight black plastic cylinders of different diameters. You are asked to group the cylinders, take data, organize it, graph it, and create an equation relating the mass to the length and diameter of the spheres.
Discover Density Set 012–07192A 5. Determine an equation that represents the data. Use one or more of the methods outlined in the previous examples. Your instructor may tell you which method(s) to use. It is not necessary to evaluate the constant in the equation at this time. Procedure (Group 2) 1. For the other group of cylinders, create a table to record the length and mass of each. The diameter of each cylinder in this group should be the same. Record the length in centimeters.
012–07192A Discover Density Set Specificat i o n s for the Pa rt s cm3 cm3 cm3 cm3 AB1 (a) (b) (c) (d) 5.02 g; 9.83 g; 14.73 g; 20.92 g; 0.95 0.95 0.95 1.90 cm cm cm cm * * * * cm cm cm cm = = = = 1.88 3.66 5.49 7.89 AB2 (a) (b) (b) (b) 4.47 g; 10.29 g; 14.81 g; 19.62 g; 1.31 1.31 1.31 1.31 cm cm cm cm * 1.31 cm * 1.93 cm * 1.31 cm * 4.45 cm * 1.31 cm * 6.38 cm * 1.31 cm * 5.59 cm = = = = 3.31 cm3 7.62 cm3 10.94 cm3 14.7 cm3 0.95 0.95 0.95 1.90 cm cm cm cm * * * * 2.08 4.05 6.08 2.
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012–07192A Discover Density Set T eacher’s Notes Spheres Finding the equation that describes the experimental data (spheres) From the experimental data, the following relationships are shown to exist: mass is proportional the diameter cubed therefore: mass = C * diameter3 where “C” is some constant Solving for “C”: C = mass / diameter3 Substituting values for smallest sphere: C = 2.48 g / (1.59 cm)3 = 0.617 g/cm3 Rechecking with values from the next to largest sphere: C = 4.81 g / (2.22 cm)3 = 0.
Discover Density Set Cylinders 012–07192A Finding the equation that describes the experimental data From the experimental data, the following relationships are shown to exist: mass is proportional to the diameter squared mass is proportional to the length therefore: mass is proportional to the (diameter squared * length) this means: mass = C * diameter squared * length where “C” is some constant Example: Calculating “C” for the item in A4: C = mass / (diameter squared * length) = 11.38 g/ (19.1 cm2 * 2.
012–07192A Discover Density Set Technical Support Feedback Contacting Technical Support If you have any comments about the product or manual, please let us know. If you have any suggestions on alternate experiments or find a problem in the manual, please tell us. PASCO appreciates any customer feedback. Your input helps us evaluate and improve our product.
