Experiment 02

MEASUREMENT

ANALYSIS

Complete the information and questions on the Worksheet.

A. Measurements with Meter Stick

1.     Calculate the average values of the length and the diameter of all the cylinders from the measurements taken with the meter stick, and enter the values in the appropriate cells in the data table covering cells C12 through H27.

2.     Calculate the uncertainty in each average value and enter the value in the cells indicated. Recall that the uncertainty resulting from a series of measurements of the same quantity is the standard deviation of the mean, sm. The relation to apply is:

3.    Calculate the volume of all the cylinders from the average lengths and diameters, and enter in cells I15 through I27.
Use the formula for the volume:

V = A·L = p r2 L = p d2 L/4.

4.    Calculate the uncertainty in the volume DV, using the measured uncertainties in the average length DL, and average diameter Dd for each cylinder, and enter in cells J15 through J27.

The relation to apply is:

DV = ( 2Dd/d + DL/L ) V.

5.    Find the average mass for each cylinder, and enter the values in cells D41 through D53. Use sm to determine the Uncertainty in the average mass values, and enter the results in cells E41 through E53.

6.    Knowing the average mass and its uncertainty Dm, the volume and its uncertainty DV, calculate the density r, and the uncertainty in the density Dr, for each cylinder in cells J39 through K45.
The relations to apply are:


r = M / V and Dr = (Dm / m + DV / V) r

B. Measurements with Vernier and Micrometer Calipers   1.     Calculate the average values of the length and the diameter of all the cylinders from the measurements taken with the calipers, and enter the values in cells D93 through G105. Once again, compute the sm values to determine the uncertainty in the average values. Enter these uncertainties in cells E93 through H105.

2.    Calculate the volume of all the cylinders from the average lengths and diameters, and enter in cells I93 through I105.
Use the formula for the volume:

V = A·L = p r2 L = p d2 L/4.

3.    Calculate the uncertainty in the volume DV, using the measured uncertainties in the average length DL, and in the average diameter Dd for each cylinder, and enter in cells J93 through J105 .

The relation to apply is:

DV = ( 2Dd/d + DL/L ) V.

4.    Copy the average mass values you obtained earlier for each cylinder in cells H39 through H45 in cells D115 through D121. Copy the volume values you obtained from cells I93 through I105 into cells E115 through E121.

5.    Knowing the average mass and its uncertainty Dm, the volume and its uncertainty DV, calculate the density r, and the uncertainty in the density Dr, for each cylinder in cells F115 through G121.
 

The relations to apply are:


r = M / V and Dr = (Dm / m + DV / V) r

6.    From the data for all the cylinders, compute:
  Enter the results in cells F124 and F126 on the Worksheet.

7.    Use the table to make a plot of average mass vs. volume for the cylinders and find the slope of the best straight line through the data. Enter the value of the slope in cell F128. The slope of this plot should represent the best value of the density by utilizing the data from all the cylinders.

8.    Compare the average density values you obtained from the caliper measurements and from the meter stick measurements, and enter the summary results in cells F133 through F136.

9.    Answer Questions 4 through 6 on the Worksheet.

10.    Submit the completed Worksheet along with all graphs as your lab report.