The Friction Coefficient

INTRODUCTION

Friction f is a force created between two surfaces. It depends on the normal force N and the friction coefficient μ

f_s = μ_sN = μ_smg

μ_s - coefficient of static friction

f_k = μ_kN = μ_kmg

μ_k - coefficient of kinetic friction

Experiment

Equipment

Wooden blocks with hooks
Selected surfaces
- 1. Wooden board
  2. Glass
  3. Cardboard
  4. Metal
  5. Brick/stone
The force sensor and LabQuest interface
Weights (Figure 1)

Figure 1. Lab equipment.

Experimental Procedure

First Trials

Connect the force sensor to the LabQuest interface. Choose the Graph tab in the top menu. Use the green arrow in the lower left corner to start recording data.

Place a wooden block on the board. Hook the force sensor to the wooden block wood and pull horizontally until the block begins to move. Continue slowly with constant force as shown in Video 2.

As simple as it sounds, pulling the wooden block in a proper way is not easy. Perform a few trials until you get a graph similar to the one shown in Figure 3.

Video 2. Experimental procedure.

Figure 3. An ideal graph with a clearly visible area of static and kinetic friction

Reading the Graphs

The first part of the graph is recorded when the wooden block starts moving. Static friction is measured as the highest point of the peak. To find its value, mark the peak area, go to Analyze > Statistics, and find the maximum (in Figure 4, it is 10.689 N).

The next part of the graph shows kinetic friction. Kinetic friction is measured as the mean of the plateau next to the peak. Mark the plateau area, go to Analyze > Statistics, and find the mean (in Figure 5, it is 7.416 N).

Figure 4. Static friction statistical analysis

Figure 5. Kinetic friction statistical analysis

Part A. Wood-wood Friction Coefficient

Investigate the frictional force as the function of weight. In order to do that, repeat the procedure of measuring the frictional force for various masses placed on the wooden block. Collect the data in Table 1 on the Lab Worksheet.

Column 1 lists weights placed on the wooden block.

Column 2 is the total mass of the wooden block and added weights.

Column 3 is to calculate the normal force. Do that by multiplying mass from column 2 by gravitational acceleration, 9.81 m/s².

Column 4, "Static Friction", is for the force of static friction read based on the graph analysis as shown in Figure 4.

Column 5, "Kinetic Friction", is for the force of kinetic friction read based on the graph analysis as shown in Figure 5.

Friction Coefficient Table

Figure 6. Data Collection Table

Figure 6. Data Collection in the Lab

Data Analysis

Step One. Plot data from the table in two separate series.

You can graph the points on paper or use Desmos graphing calculator.

The frictional force determined based on graph analyses goes on the vertical axis. Weight from Column 2 of the Data Collection Table goes on the horizontal axis.

Plot data from Column 4 in one series and column 5 in a separate series as shown in Figure 7.

Step Two. Read the friction coefficients from the graph.

Read the slope of the line. The value of the slope is the friction coefficient.

On paper, select two points and follow the "rise-over-run" method (see Figure 8).
In Excel or Desmos, you can do that by performing a simple regression (Figures 9 and 12).

Figure 7. The concept of graphing the frictional forces in two separate series.

Figure 8. Sample graph by hand.

Figure 9. Sample graph in Excel.

Step Three. Compare the results with the accepted value.

The coefficient of static friction is well-defined and its values for various materials can be found in numerous sources. Its value for wood-on-wood is between 0.25 to 0.50, depending on the wood and air humidity.

The published values of the kinetic friction coefficient vary. The reasons for that inconsistency include various measurement methods and external conditions, such as humidity and temperature. Also, the dynamics of sliding materials change the conditions during the experiment, which creates new challenges for measurement. For the purpose of this lab, the accepted value of the kinetic friction coefficient for wood-on-wood is 0.2.

Part B. Friction Coefficient for Different Materials

Repeat the same investigation for different surfaces. Choose one of the available options:

wood-brick
wood-cardboard
wood-concrete
wood-cork
wood-glass
wood-metal
wood-stone
wood-wood

Figure 10. Glass on wood

Figure 11. Wood on glass

As shown in Figures 10 and 11, you can investigate friction between two surfaces, A and B, sliding surface A on surface B or surface B on surface A. The friction coefficient should be the same.

Figure 12. Wood-cork sample graph in Desmos.

APPENDIX

Static Friction Coefficients for Wood

Wood on Brick - 0.60

Wood on Cardboard - 0.30

Wood on Concrete - 0.62

Wood on Cork - 0.50

Wood on Glass - 0.22

Wood on Metal- 0.20 to 0.60

Wood on Stone - 0.20 to 0.40

Wood on Wood - 0.25 to 0.50

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