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Lab 1: Relationship Between Mass and Volume Faith Eastwood Natalia Sedykh Phys. 122

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Purpose What is the relationship between mass and volume for a copper cylinder.

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Theory There will be a direct linear relationship between volume and mass. As Volume increases mass will increase.

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Materials and Procedures Materials: Balance scale, solid copper cylinders, micrometer Procedures: – Measure the mass using a balance scale. – Measure the length and the diameter using the micrometer – Calculate the volume using the formula (3.14r^2)(h) – Repeat steps 1-3 with each cylinder

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Uncertainty Uncertainty: To determine the uncertainty of our measurement devices we took 10 readings with the balance scale and 10 readings with the micrometer. Uncertainty for length: Average 1.289 cm Max 1.230 cm Min 1.226 cm Uncertainty.063 cm Uncertainty for mass: Average 29.29 g Max 29.31 g Min 29.25 g Uncertainty.04 g

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Data and Sample Calculation Measured DataDerived Mass g +/-.04 Height cm +/-.063 Diameter cm +/-.063 Volume Cm^3 23.901.2281.2681.550 29.212.6001.2663.271 57.535.1001.2906.662 Sample calculation for volume V=Πr^2*h V=3.14*.634cm^2*1.228cm V= 1.550 cm^3

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Graph

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Analysis From our graph we can tell that there is a positive linear relationship between volume and mass. As the volume of our cylinders increased the mass increased as well. The equation for the line is y=8.97g/cm^3 This means that for every increase in volume of 1 cm^3 the mass increased by 8.97 g. The units for our slope, g/cm^3) are also the units for density. Meaning that the sample of copper that we measured had a density of 8.97g/cm^3. When we looked up the density of copper online we found numbers between 9.84-9.92 g/cm^3.

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Conclusion Our theory that we would see a positive linear relationship between volume and mass. As you can see in our graph we did find a linear relationship between mass and volume. We predicted that if the volume doubled the mass would also double. We saw that for our second and third data points but not for our first. We suspect that there was measurement error with our first data point. Ideally we should have taken more measurements, but there were not any more copper samples available.

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Propagation of uncertainties Formulas and graphs.

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