I. A student measured with Vernier caliper the necessary dimensions of the 3D rectangular wood object to calculate object's volume and propagate its error. The Vernier caliper is precise to 0.05 mm, so many of the measurements gave the same results. Each dimension was measured 6 times. The collected data is provided in table below.
Table 1: Rectangular wood object
|
width, mm
|
height, mm
|
length, mm
|
|
49.10
|
24.60
|
102.00
|
|
49.20
|
24.70
|
102.15
|
|
49.10
|
24.90
|
101.90
|
|
49.10
|
24.90
|
102.00
|
|
49.05
|
24.60
|
102.15
|
|
49.10
|
24.90
|
102.15
|
1) Enter the acquired data in Logger Pro. Use Logger Pro to find the mean value of each dimension and the standard deviation of measurements (STAT function). Print and attach it to this PreLab or insert below the printscreen of the graphs made in Logger Pro. Be sure all the columns are labeled correctly. Be sure that all data is legible to read.
2) Using the standard deviation obtained in Logger Pro in the above question, calculate below the standard error for each dimension (standard deviation of the mean).
Write/type the equation used to find standard deviation of the mean.
3) Calculate object's volume. The standard (random) error in volume will be propagated through the random error in each of the dimantions. Use partial derivative approach to propagate the error. Below, be sure you write/type the equations used and show numbers that are plugged in.
4) Report final result in centimeters cube in the correct format.
II. The relationship between mass and diameter of a sphere is an example of "model". This well-known cubic relationship is studied in the second part of this lab experiment.
The measurements of masses and mean diameters for 5 clay spheres are provided in the table below:
Table 2: Clay spheres
|
# of sphere
|
mass, g
|
Mean diameters, cm
|
|
1
|
120.5
|
5.135
|
|
2
|
56.1
|
4.03
|
|
3
|
35.5
|
3.43
|
|
4
|
25.3
|
3.1
|
|
5
|
15.2
|
2.52
|
1. Calculate density of sphere # 1 only.
2. Enter the acquired data in Logger Pro. Create two new calculated columns ln (Diameter) and natural log ln (mass). Plot ln (Diameter) vs ln (mass). Apply linear fit to the graph. Print and attach it to this PreLab or insert below the printscreen of the graphs made in Logger Pro.
3. Using the slope of the ln (Diameter) vs ln (mass) graph find the power of the diameter for a case when mass of sphere is a function of the diameter.