### Summary

Using the same method for measuring friction that was used in the previous lesson (Discovering Friction), students design and conduct experiments to determine if the amount of area over which an object contacts a surface it is moving across affects the amount of friction encountered.*This engineering curriculum meets Next Generation Science Standards (NGSS).*

### Engineering Connection

Engineers must understand how friction affects a number of situations, such as the bottom of skis in which friction is a disadvantage to hiking boots where friction provides traction. An automobile disc brake slows a car when brake pads on either side squeeze the round surface (the wheel's rotor) shown in the nearby image. The process is very similar to the way the caliper hand brakes of a bicycle squeeze the bicycle's tire rims. The friction generated impedes the rotation of the wheel, causing it to rotate more slowly until it stops altogether.

### Pre-Req Knowledge

Students should be able to measure and calculate the areas of rectangles, circles, and rings (annuli). You may need to review how to find the area of a circle (A=Pi*r^{2}) and how to find the area of a ring (A=Pi*R^{2}-Pi*r^{2}), where R is the outer radius of the ring and r is its inner radius).

### Learning Objectives

After this activity, students should be able to explain that, due to molecular attractions between some types of surfaces, the amount of friction that occurs between them varies in proportion to the amount of surface area in contact.

### More Curriculum Like This

**Factors Affecting Friction**

Based on what students have already learned about friction, they formulate hypotheses concerning the effects of weight and contact area on the amount of friction between two surfaces.

**Discovering Friction**

With a simple demonstration activity, students are introduced to the concept of friction as a force that impedes motion when two surfaces are in contact. Then, in the associated activity, Sliding and Stuttering, they work in teams to use a spring scale to drag an object such as a ceramic coffee cup ...

**A Tale of Friction**

High school students learn how engineers mathematically design roller coaster paths using the approach that a curved path can be approximated by a sequence of many short inclines. They apply basic calculus and the work-energy theorem for non-conservative forces to quantify the friction along a curve...

**Red Light, Green Light: Forces of Friction, Roads & Tires**

Building upon their understanding of forces and Newton's laws of motion, students learn about the force of friction, specifically with respect to cars. They explore the friction between tires and the road to learn how it affects the movement of cars while driving.

###
Educational Standards
Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

###### NGSS: Next Generation Science Standards - Science

- Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### Common Core State Standards - Math

- Summarize numerical data sets in relation to their context, such as by: (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Reporting the number of observations. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve real-world and mathematical problems involving area, surface area, and volume. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Represent and analyze quantitative relationships between dependent and independent variables. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. (Grade 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### International Technology and Engineering Educators Association - Technology

- Brainstorming is a group problem-solving design process in which each person in the group presents his or her ideas in an open forum. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Some technological problems are best solved through experimentation. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Design and use instruments to gather data. (Grades 6 - 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### North Carolina - Math

- Solve real-world and mathematical problems involving area, surface area, and volume. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Represent and analyze quantitative relationships between dependent and independent variables. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Summarize numerical data sets in relation to their context, such as by: (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. (Grade 8) Details... View more aligned curriculum... Do you agree with this alignment?
- Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. (Grade 8) Details... View more aligned curriculum... Do you agree with this alignment?

###### North Carolina - Science

- Predict the effect of a given force or a change in mass on the motion of an object. (Grade 5) Details... View more aligned curriculum... Do you agree with this alignment?
- Understand motion, the effects of forces on motion and the graphical representations of motion. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Explain the effects of balanced and unbalanced forces acting on an object (including friction, gravity and magnets). (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Understand the relationship between forces and motion. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Classify frictional forces into one of four types: static, sliding, rolling, and fluid. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?
- Explain work in terms of the relationship among the applied force to an object, the resulting displacement of the object and the energy transferred to an object. (Grades 9 - 12) Details... View more aligned curriculum... Do you agree with this alignment?

### Materials List

- spring scales, preferably having a 500 g capacity and 5-10 g accuracy, one per team of 2 to 4 students; Ohaus makes one that works well for this exercise; it is available from suppliers such as Ward for about $6
- ceramic coffee mugs, one per team of 2-4 students (ask students to bring these from home or purchase them from thrift stores)
- scissors (one per team)
- tape (masking or wide transparent), one roll per team or one roll shared between two teams
- string, about 30 cm per team
- cardboard or poster board, enough for about 1 square foot per group
- Styrofoamâ„¢ picnic plates, about four per group, and/or stiff glossy paper, laminated paper or overhead transparency plastic; enough for 1-2 square feet per group
- rulers, one per group

### Introduction/Motivation

Since students have already formulated hypotheses concerning the effects of contact area on friction (as part of the accompanying lesson), little further introduction to the activity is needed.

Remind them, however, about the importance of controlling variables in scientific experiments. In this case, contact area is the only thing that should differ each time they drag their coffee mugs across a surface and measure the resulting frictional force. Other variables, such as the type of surface used and the weight of the mug, must be controlled, that is, not varied during the experiment.

### Vocabulary/Definitions

coefficient of friction: An empirically derived quantity for a pair of surfaces that is equal to the amount of friction measured divided by the weight of the object being moved.

friction: A resistance to motion that occurs when two surfaces are in contact with each other.

kinetic friction: The resistance to motion that occurs once one surface is in motion, sliding against another surface.

static friction: The resistance to motion that must be overcome in order to allow one surface to begin sliding against another surface.

### Procedure

Part 1: Designing the Experiment

Although students should already be familiar with the basic method for measuring friction using spring scales and coffee mugs, they still need to make several decisions in order to design an experiment to test for the effects of contact area on friction. Write the following list of questions on the board (or provide them in a handout):

- How much area of contact will you use? Will you test just one contact area, or several?
- What material will you attach to the bottom of your mug, and what surface will you use for dragging your mug over?
- How many trials will you do?
- Will you measure and record both types of friction (static and kinetic)?
- How will you record your data?

Then have students meet in their groups to discuss these questions. Once all members of a group agree on the answers, and you have verified that the answers are reasonable, the group should be ready to conduct its experiment. Encourage different groups to test different materials, instead of having the entire class test Styrofoam^{TM}, for example.

Part 2: Conducting the Experiment

Provide groups with the materials and direct students to conduct their experiments. Direct students to use the Does Contact Area Matter? Worksheet to record their data and results.

Part 3: Analyzing the Data

Remind students that scientists typically report the results of their experiments in the form of graphs. Have students use their data to prepare graphs similar to the one shown in the Lesson Background and Concepts for Teachers section in the associated lesson. Then ask them to write a paragraph describing what their data show about how contact area affects friction.

### Attachments

### Investigating Questions

As students design their experiments, ask questions such as:

- Why is it a good idea to use only one pair of surfaces for these experiments, i.e., one material for the surface attached to the bottom of the mug and one surface over which the mug is dragged? (Answer: Since we are looking for a relationship between the amount of contact area between the two surfaces and the amount of friction that results, it is important to control all other variables. Therefore, it is important to not vary the type of surfaces being tested during the experiment. Instead, only a single pair of surfaces should be used for one experiment. However, a second set of materials could be used for a second set of experiments.)
- Why is it necessary to test at least two different amounts of contact area? (Answer: Since it is not yet known what the effect of contact area will be, by testing several different amounts we can see if there is a consistent trend based on the amount of contact area.)
- Why is it a good idea to measure and record both the static and kinetic friction? (Answer: Since we don't yet know what will happen when contact area varies, we don't know if it will affect both static and kinetic friction, or just one, or neither. Measuring both will give a more complete picture of how contact area affects friction.)

As students conduct their experiments, ask questions such as:

- Based on what you are seeing so far, what effect does contact area seem to have on friction?
- Based on what you already know about friction and what causes it, why do you think increasing (or decreasing) contact area has the effect that it does?

### Assessment

Use the first three Investigating Questions to check for understanding of the process of scientific inquiry involved in this activity. Also, check to see that students are reading the spring scales with reasonable accuracy and are accurately recording their data.

As students prepare their graphs, check to see that they put the dependent variable (friction force) on the y-axis and the independent variable (contact area) on the x-axis. Also check to see if their graphs also include the origin (0,0), labels on the axes (including units), and a legend if both the static and kinetic friction are shown in one graph.

### Activity Extensions

Have students repeat their experiments using a different type of surface for either the bottom of the mug, or the surface over which the mug is being dragged. Depending on the pair of surfaces involved, they may find that contact area does or does not have an affect on the amount of friction that is generated, depending of the relative importance of molecular attractions between the particular surfaces chosen.

### Contributors

Mary R. Hebrank, project writer and consultant### Copyright

© 2013 by Regents of the University of Colorado; original © 2004 Duke University### Supporting Program

Engineering K-PhD Program, Pratt School of Engineering, Duke University### Acknowledgements

This content was developed by the MUSIC (Math Understanding through Science Integrated with Curriculum) Program in the Pratt School of Engineering at Duke University under National Science Foundation GK-12 grant no. DGE 0338262. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.

This activity was originally published, in modified form, by Duke University's Center for Inquiry Based Learning (CIBL). Please visit http://www.biology.duke.edu/cibl for information about CIBL and other resources for K-12 science and math teachers.

Last modified: August 16, 2017

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