Physics Lab 4

Lab 4 Friction – Data Analysis

Data Analysis

The same friction experiment was conducted as you did in class. Three sets of data were obtained.

Data set 1 is comprised of 10 repeated friction force measurements for the same normal force 𝑁1 =

20.80N. Data set 2 is also comprised of 10 measurements but for a different normal force 𝑁2 =

6.08N. Data set 3 has the same normal force 𝑁1 = 20.80N as data set 1, but the wood block has its

narrow wood surface as the contact surface, the contact area is 32.8cm2; whereas, in Data set 1, the

contact area is 65.5cm2. The experiment setups of the 3 data sets are shown in Figure 1. Please use

the data sets to answer the following questions. You may need to refer to the lab manual and the

separate document Uncertainty.docx for some information.

Figure 1: Experimental setups for the 3 sets of data for processing. The 3 data sets were obtained under the following conditions respectively, (a), great normal force and large contact area; (b), small normal force and large contact area; (c), large normal force and small contact area.

Data Set 1

(a)

(b)

(c)

Normal Force (N) 20.80N Contact Area (cm𝟐) 65.5cm2

Data Count 1 2 3 4 5 6 7 8 9 10

Max static friction force (N)

5.53 4.76 4.79 5.28 5.56 5.28 5.62 5.22 5.43 5.07

Kinetic friction force (N)

3.40 3.30 3.34 3.36 3.36 3.38 3.41 3.26 3.28 3.42

Data Set 2

Normal Force (N) 6.08N Contact Area (cm𝟐) 65.5cm2

Data Count 1 2 3 4 5 6 7 8 9 10

Max static friction force (N)

1.98 1.59 1.34 1.43 1.56 1.53 1.71 1.68 1.50 1.80

Kinetic friction force (N)

1.00 0.99 0.92 0.96 0.95 0.96 0.99 0.94 0.96 0.97

Data Set 3

Normal Force (N) 20.80N Contact Area (cm𝟐) 32.8cm2

Data Count 1 2 3 4 5 6 7 8 9 10

Max static friction force (N)

5.68 5.74 4.95 5.13 5.62 5.22 4.91 5.25 5.22 5.37

Kinetic friction force (N)

3.59 3.34 3.25 3.33 3.51 3.17 3.24 3.31 3.46 3.30

Question 1: (5 points)

Please process Data Set 1 in Excel, and list the results below.

Data Set 1

Average Standard Deviation Standard error

Static friction coefficient

Kinetic friction coefficient

Question 2: (5 points)

Please process Data Set 2 in Excel, and list the results below.

Data Set 2

Average Standard Deviation Standard error

Static friction coefficient

Kinetic friction coefficient

Question 3: (5 points)

Please process Data Set 3 in Excel, and list the results below.

Data Set 3

Average Standard Deviation Standard error

Static friction coefficient

Kinetic friction coefficient

Question 4: (5 points)

Please calculate the 95% confidence range for all friction coefficients and record them below in the

format of ±95% range.

Data Set 1 Data Set 2 Data Set 3

Static Friction Coefficient

95% Confidence Range

Kinetic Friction Coefficient

95% Confidence Range

Question 5: (5 points)

The simplified friction theory says that the static and kinetic friction coefficients 𝜇s and 𝜇k are

independent of the normal force applied, and their values do not change regardless of the normal

force applied. Our data sets 1 and 2 can help us determine how well the theory matches the reality,

since the only different parameter between the two sets is just the normal force. Do the coefficients,

both static and kinetic respectively, stay the same within the confidence range? (This is to ask if there

is overlap of the confidence ranges? If there is, the coefficients have a chance to be the same;

otherwise, we have high confidence they are different.) Please write complete sentence and cite your

results to answer the question.

Question 6: (5 points)

The simplified friction theory says that the static and kinetic friction coefficients 𝜇s and 𝜇k are

independent of the size of the contact area. Our data sets 1 and 3 can help us determine how well the

theory matches the reality, since the only different parameter between the two sets is just the contact

area. Do the coefficients, both static and kinetic respectively, stay the same within the confidence

range? Please write complete sentence and cite your results to answer the question.

Lab 4 Report – Presenting Data Table

Using table is a convenient technique to organize, present and analyze information. When used correctly, tables can help the reader

quickly understand abstract concepts, trends, etc. hidden within the information. Usually, a data table is accompanied with some

description/explanation/discussion to build a narrative.

Please refer to the example on the next page.

Requirements:

In this report, please make two data tables and write a paragraph to address the following questions. Please make one table for each

question. You may use the questions in the Data Analysis as a starting point.

1. Do the friction coefficients, static and kinetic, remain the same regardless of the normal force applied? 2. Do the friction coefficients, static and kinetic, remain the same regardless of the contact area?

Table

Item 0 points 2 points

Data relevancy Data in the table is inadequate or irrelevant to address the questions.

Data in the table is adequate and relevant to address the questions.

Data organization Data is poorly organized. Data is organized for easy reading and to facilitate comparison of number in order to address the questions.

Table title and numbering

Table numbering and title are missing. Table is correctly numbered, and the title briefly summarizes the data. Table title and numbering appear in bold font.

Paragraph

Item 0 points 4 points

Table reference The paragraph does not cite data values in the table. The paragraph cites the data values in the table to address the question.

Logic (6 points) The narrative in the paragraph is not supported by the data in the table.

The narrative in the paragraph is supported by the data in the table.

Language Informal language with more than 3 errors and awkward content flow were used.

Formal language of natural content flow and with no errors were used.

Sample table presentation

Table 1 below lists the average salary for some major programs for Lawrence Technological University (LTU) alumni. The data was obtained from the website www.payscale.com. Please note that this table does not include all major programs offered at LTU. Although the website claims that the data was updated on Aug 24, 2019, there is no way we can verify its reliability. The website gathered data through alumni self report; and the number of participating alumni seems very small (683); therefore the numbers cannot faithfully reflect the average salary landscape for LTU graduates. However, the numbers are in line with the national trend that art majors general earn less than engineering majors. For example, the alumni of Bachelor of Fine Arts earn the lowest average salary in the table, $49,500; meanwhile the two highest salaries, $100,600 and $110,960 go to two bachelor degrees of engineering. In addition, the table does reflect the well-known strength of LTU – its engineering programs; most of the higher average salary numbers belong to engineering related programs.

Table 1: Average Salary by major for Lawrence Technological University alumni

Major Average Salary ($)

Bachelor of Architecture 58,696

Bachelor of Arts 67,664

Bachelor of Business Administration 91,000

Bachelor of Engineering 94,972

Bachelor of Engineering Technology 110,960

Bachelor of Fine Arts 49,500

Bachelor of Science, Architecture 65,000

Bachelor of Science, Civil Engineering 67,619

Bachelor of Science, Electrical Engineering 100,622

Bachelor of Science, Mechanical Engineering 87,290

Bachelor of Technology 96,500

Content in the table is

referred to several times.

The table is numbered for easy reference; and

the title briefly summarizes the data content. Data is well organized in two

columns for easy read.

The paragraph describes the data source, and refers to the numbers to stress its

merit despite its questionable reliability.