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Properties of Materials Thomas Ulep, Evelyn Dial, Clara Jung, Trevor Gratz Pink Group September 29, 2011 Physics 122

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Question: Hypothesis: For a group of objects of the same material, the mass and volume are directly proportional. The proportionality constant is the material’s density. What is the relationship between mass and volume of various objects made of the same material?

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Predicted Mass versus Volume Graph From College Physics, pg. 406: “The mass density is independent of the objects size. That is, mass and volume are parameters that characterize a specific piece of some substance…where as mass density characterizes the substance itself.” Mass (g) Volume (mL)

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Procedure: Materials: 2 small brass cylinders 2 large brass cylinders 2 brass bars 2 brass cubes beam balance graduated cylinder water Measure the mass of one of the objects in grams.Then drop the object in a graduated cylinder containing water. Record the initial and final water levels in mL. Remove the object from the water and dry it with a paper towel. Repeat these steps with each of the objects, then graph all data collected.

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Data: Object Mass (g) ± 0.05g Initial Volume (mL) ± 0.2mL Final Volume (mL) ± 0.2mL Displacement (mL) ± 0.2mL One Small Cylinder15.15051.91.9 Two Small Cylinders30.25053.83.8 One Big Cylinder54.65763.53.5 Two Big Cylinders109.3577013 One Big Rectangle6859.367.78.4 Two Big Rectangles106.267.78012.3 One Square Block140.9111413117 Two Square blocks278.8511415036

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Graph: Equation of Line: M = 7.72 g/mL (V)

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Uncertainty : All Values: n= 10 (mL)Without Outlier: n = 9 (mL) Maximum Value2.1 mL Minimum Value1.2 mL1.7 mL Average1.8 mL1.9 mL Difference from Average (max.)2.1 – 1.8 = 0.3 mL2.1 – 1.9 = 0.2 mL Difference from Average (min.)1.8 – 1.2 = 0.6 mL1.9 – 1.7 = 0.2 mL Average ± Uncertainty1.8 ± 0.6 mL1.9 ± 0.2 mL All Values: n= 10 (g)Without Outlier: n = 9 (g) Maximum Value15.23 g Minimum Value15.10 g15.15 g Average15.17 g15.18 g Difference from Average (max.) 15.23 – 15.17 = 0.06 g15.23 – 15.18 = 0.05 g Difference from Average (min.) 15.17 – 15.10 = 0.07 g15.18 – 15.15 = 0.03 g Average ± Uncertainty15.17 ± 0.07 g15.18 ± 0.05g

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When comparing objects composed of the same material, the mass of each object is directly proportional to the volume. Constant of proportionality is the density Graph was a straight line with the equation: mass (g) = [density (g/mL)] [vol (mL)] **Derived from the generic equation of a line, y = mx + b. Slope of the line is equal to density. Analysis:

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Density is a measure of mass per unit volume. Different materials have different densities which will affect the slope of the line. Examples: Lead has a high density ----> slope of mass vs. volume will be steep. Plastic has lower density ----> slope will be flatter Analysis continued...

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In conclusion, mass and volume values of various objects of a particular material are directly proportional. When graphed, these data points form a straight line whose slope is equal to the density of that material.

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