Unknown Block Lab

Determination of Unknown Block Material and Uncertainty Analysis

Xuan Wang

TA: Saurabh Chawdhary

ME4031W
Lab Section 014 4:40PM Wednesday

2/10/2013
Abstract

People discovered many methods to determine the properties of unknown materials (harness, density, or elastic modulus etc.). In this lab, the task is to find the density of an unknown block. If the dimensions and mass of unknown block can be obtained, the density can be calculated by block mass over block volume. After comparing the result density value to a reference chart, the specific material category can be determined. Dimensions can be measured by using a caliper and a micrometer and mass can be determined by putting the block onto an electronic balance. All equipments…show more content…
Each size was measured six times. So we had 36 data points in total. Then, we calibrated the micrometer with six different size of gage block (0.1, 0.101, 0.12, 0.3, 0.4, 0.5 inch). Each gage block was measured six times also. Therefore, we had 36 data points for micrometer calibration. The caliper was calibrated in very similar way as micrometer. The six gage blocks caliper used were 0.105, 0.11, 0.16, 0.3, 0.5, 2 inch. Record all data in lab notebook.
After the calibration, select one of unknown blocks in the shelf. In this lab, block No.5 was chosen. Use caliper to measure the length of the block and diameter of the hole. Use micrometer to measure the height and the width of block. Finally, use scale to measure the mass of the block. Each dimension was measured six times. Therefore, we totally had 30 data points.
After all measurements were done, average the data for each variable. By Equation 3, the density could be calculated. Plus, the totally uncertainty could be calculated based on calibration results. Combine the density and its uncertainty, a range of unknown block’s density could be…show more content…
So the resolution error value would not be included in the precision uncertainty calculation. The equation of t- value is shown in below: (7)

The degree of freedom was obtained by Equation 8. v=N-1 (8)
The total random error was calculated by root sum of squares (RSS) shown below up=±upi2 (9)
The bias error was equal to the bias error of instruments. ub=ubi2 (10)
The total uncertainty was the square root of total random error square plus total bias square. ux= ub2+up2 (11)
The total uncertainty could be found by using Partial Derivative Method. The general equation is shown below uρ=(∂ρ∂mum)2+(∂ρ∂lul)2+(∂ρ∂huh)2+(∂ρ∂wuw)2+(∂ρ∂dud)2 (12)

The partial derivative for each variable is shown below:

∂ρ∂m=1hlw-πd24w (13)

∂ρ∂l=-hmw(hlw-πd24w)2