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Lab 2 Density 72 out of 85.docx

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Arizona State University
PHY 122

Lab 2: Diameter, Mass and Density By: T.A: Monday at 2:00 p.m Abstract: This experiment was performed in order to demonstrate how density is related to mass and diameter and how mathematical models can be made to model real life scenarios. The diameter was measured six times for six spheres of different sizes and the mass was measured once for the ρ=ρ ∇ρ spheres (all made of the same material). The density was found using averag+/- , 6m ρ= 3 ∇ ρ where π∗d and is the error propagation for the density equation. The g density was found to be 1.67 +/- .02 cm3 .Then, the density of the sphere was approximated by comparing how fast it sunk to other objects with known densities. After plotting diameter cubed versus the mass a best fit line and the slope of the line (of graph one in the appendix) was found which determined the ρaverageρ respectively. The same approach was used for the ln graph model and the density was found, using that model, to be 1.78 +/- .02 g . g cm 3 For the ln plot, the density was equa1.65 +/- .05 cm 3 . These results show that using any of the models will give you a fair estimate for what the density of an object is. The results also suggest the ln plot more fairly represented the actual density. Objective: The goal of this lab is to find the density of spheres of clay and then find a model function for the relationship between mass versus diameter using both a linear and a ln-ln plot. Equipment: The equipment used in this lab was a scale to measure the weight, a Vernier caliper to measure the diameter of the spheres and a container with water to test how fast different objects sank when placed in water. Procedure: The diameters of each of the six spheres were recorded six times using the Vernier caliper. The mass of each sphere was measured once using the scale. A qualitative experiment was then done to approximate the density. The qualitative experiment was conducted by dropping objects with known densities in a container of water with the unknown density of the clay. The clays’ speed was compared to the other objects to get a rough estimate of the density of the clay. Using graphical analysis, two different plots (one that compared the mass to the diameter cubed and one that compared the ln(mass) versus the ln(diameter)) were made that simulated the relationship between the mass and diameter of the clay spheres. This was then checked with the qualitative experiment to verify that the results obtained were reasonable. Results Part 2: As several different shapes with different densities were dropped into a tank of water, it was g g found that the density of the clay should be between 1.07 3 and 7.3 3 cm cm Part 3&4: Figure 2: Figure 3: DataAnalysis: Part 1: ρ Density ( ρ ) = average+/- ∇ ρ ρ = 6m averagπ∗d 3 *mass is the average mass and d is the average diameter ρ Example Calculation averagfor sphere 3: ρ average∗95.34 =1.67 g π∗4.782 3 cm3 m n ∇ρ given the equation f =cx ∗y : ∇F 2 ∇x 2 ∇y 2 ( f ) = m ∗( x ) + n∗( y ) 2 2 ∇ρ=∇F=f∗ ∣m∣∗(∇x ) ∣n∣∗(∇ y ) √ x y ∇F =the error propagation in the density; f= the average density; m=expon=error in mass; x=average mass of the sphere; =standard deviation of mean for the diameter; y=average diameter ∇ ρ Example calculation for for sphere 3: .01 2 .026 2 g
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