Physics lab report 1 measurements PDF

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Summary

lab report for first experiment called measurements (received perfect score)...

Description

Siron Mani 1.31.19 Measurements, Propagation of Error, and Density

Objective The purpose of this experiment is to practice and understand how to use various tools of science such as: rulers, Vernier calipers, micrometer calipers, and platform balances as well as figure out uncertainties in our data from errors. Theory Every measurement taken has some kind of uncertainty to it. This is because of limitations from the actual instrument, potential for human error, and the sample being measured. For this particular lab, the following instruments were used: the ruler, the Vernier caliper, and the micrometer. The ruler is the least precise and the micrometer is the most precise. (A ruler’s precision is 0.5mm, a Vernier caliper’s is .05 mm, and a micrometer’s is .005 mm.) Scientific results combine multiple pieces of data each with their own errors. Because of this, it is important to understand how important each piece of data is to the final result of the experiment as well as how important it is to understand how each data piece contributes its errors into the result. Analyzing uncertainty is called “Propagation of Errors.” If data was collected from a number of different scientific tools, then the error in that quantity should be a combination of the errors for each of the individual measurements from each tool. To begin the experiment, a cylinder is appointed to a group and the measuring of its mass ensues. First, the ruler is used to measure the length and diameter of the shape. Then the Vernier caliper and lastly, the micrometer. The quantities are recorded in a table. Volume: V =π

Density: ρ=

D2 h 4

m v

Error in measured density: σ ρ = ρ √ ❑

Data

Using Ruler: Diameter: 1.5 cm Height: 2.0 cm Mass: 41.8 grams 1)

2)

D2 xh 4 1. 52 = π∙ x 2.0 cm 4 = π ∙ 0.5625 x 2 = 3.5325 c m2 ❑❑ V =π ∙

ρ=

m v

41.8 3.5325 = 11.83 g/c m3 =

3)

σ ρ= ρ √ ❑ = ρ √❑ = 11.8 x 0.07 = 0.838 g/c m3

Using Vernier Caliper Height: 2.49 mm (0.249 cm) Diameter: 1.69 mm (0.169 cm) Mass: 41.8 grams D2 h 4 1.69 mm2 V =π (2.49 mm) 4 = 3.31 m m3 (or 4.944 cm^3) 1)

V =π

2)

ρ=

m v

41.8 g 3.31 m m3 = 12.628 g/mm^3 (or 8.455 g/cm^3) =

3)

σ ρ= ρ √ ❑ ¿ ρ √❑ = 0.31599 g/mm^3 (or 0.025 g/cm^3)

Using micrometer

Diameter: 15.8 mm Height: 24.82mm Mass: 41.8 grams D2 h 4 15.8 2 V =π (24.82 mm) 4 = 4866 mm^3 (or 4.862 cm^3)

1)

V =π

2)

ρ=

3)

σ ρ= ρ √ ❑ σ ρ=0.00859 √❑ = 0.00057 g/mm^3 or 0.011766 g/cm^3

m v 41.8 g ¿ 4866 mm 3 = 0.00859 g/mm^3 (or 8.597 g/cm^3)

Metal Identification:

Ruler: ERROR Vernier caliper: BRASS Micrometer: BRASS Difference in Percentage Ruler:

|experimental value−theoretical value | theoretical value = (11.8-8.4)/(8.4) x 100% = 0.405%

x 100%

Vernier caliper:

|experimental value−theoretical value | theoretical value =(8.455-8.4)/(8.4) x 100% = 0.00655%

x 100%

Micrometer:

|experimental value−theoretical value | theoretical value

x 100%

= 0.0235%

Analysis After calculating our quantities, the densities resulted in the following: ruler was 11.8 g/cm^3, Vernier caliper was 8.455 g/cm^3, and the micrometer was 8.597 g/cm^3. There was a clear error in the ruler’s results as it was such a small number compared to the other two. The mistake could have came from the ruler or my partners and I or both. It is obvious that the micrometer is the most precise tool of measurement. After checking the appropriate table, it was evident that the cylinder was indeed made of brass.

Conclusion

This experiment revolved around the various tools of measurement as well as the calculations that followed each measurement. With these utensils and equations, we were able to obtain the diameter, the height, and the mass of a cylinder. The objective was to use our resources and discover what the cylinder was made of based on our calculated densities. The results prove that the most precise tool was the micrometer. The reason for this being that it had the smallest uncertainty compared to the ruler and the caliper. The ruler had the biggest errors and that was mostly likely due to some measurement mistake. Regardless, even if that were to be corrected, it would still be the least precise scientific tool....