# Me 3057 -Lab 2

**Topics:**Measurement, Uncertainty, Normal distribution

**Pages:**11 (3298 words)

**Published:**July 18, 2010

ME 3057 - EXPERIMENTAL METHODOLOGY & TECHNICAL WRITING

Report/Worksheet/Writing Task: Lab number 2

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LAB 2: MEASUREMENT UNCERTAINTY AND ERROR ANALYSIS

ABSTRACT

Important concepts used by engineers when measuring properties are explored in this lab, such as uncertainty and error. A 15mm gage block and an aluminum pendulum are measured to gain a better understanding of these concepts. In the first section of the lab, the calibrated dimension of the 15mm gage block is measured with 0.001” and 0.0001” micrometers along with 0.001” calipers. In the second section of the lab, the density of the gage block is found by measuring the length and the thickness of the block to find the volume along with taking the mass of the block on a scale. In the last section of the lab, the period of Pendulum A is measured along with the geometry of the pendulum. The results of the first section of the lab lead to the conclusion that less error occurs in the instruments with higher resolutions. In the next section the results show that when finding a derived value the propagated error is less when taking error based on resolution as opposed to statistical error. The error based on resolution for the density was 2.23 x 10-5 compared to the error based on statistics of 0.00101.

PART I: MEASUREMENTS OF THE DIMENSIONS OF A GAGE BLOCK

A. Experimental Results

Table A.1 presents measurements of the calibrated dimension of a 15 mm gage block taken with a 0.001” resolution caliper, a 0.001” resolution micrometer, and a 0.0001” resolution micrometer. The manufacturer specified value for the gage block is 15.00004 mm and the specified uncertainty is 0.075 mm. B. Analysis

The data set of measured values from Table A.1 is used to determine the mean values and standard deviation for the gage block. The mean, X, obtained using Equation 1 and the standard deviation, σ, measures the spread of data around the mean and is obtained using Equation 2

X=1Ni=1NXi (Eq. 1)

σ=1N-1i=1NXi-X2(Eq. 2)

where N is the number of data points and Xi is the measurement at i. Table 1 shows the mean measurements of the calibrated side of the gage block and the associated standard deviation associated with that mean value. The standard deviation is a measure of uncertainty, and the instrument with the smallest uncertainty of can be considered the most precise.

Table 1. Mean and Standard Deviation for Gage Block

| | 0.001" Micrometer (in.)| 0.001" Micrometer (mm)| 0.0001" Micrometer (in.)| 0.0001" Micrometer (mm)| 0.001" Caliper (in.)| 0.001" Caliper (mm)| | | | | | | | |

Mean| 0.5898| 14.9809| 0.5901| 14.9896| 0.5902| 14.9911|...

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