### 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 weight added incrementally to objects affects the amount of friction encountered when they slide across flat surfaces. After graphing the data from their experiments, students calculate the coefficients of friction between the objects and the surfaces they moved upon, for both static and kinetic friction.*This engineering curriculum meets Next Generation Science Standards (NGSS).*

### Engineering Connection

Engineers must understand how friction affects many situations, from the bottom of skis in which friction is a disadvantage to hiking boots where friction provides traction. Scientists must think like engineers when designing experiments, as students do in this activity.

### Pre-Req Knowledge

Students should have a basic understanding of friction and how to measure it using coffee mugs and spring scales, as was done in the previous lesson, Discovering Friction, and its activity, Sliding and Stuttering.

### Learning Objectives

After this activity, students should be able to:

- Explain that, for friction due to surface roughness, the frictional force is proportional to the weight of the object being moved across a surface.
- Calculate the coefficient of friction for an object whose weight and the measured frictional force between the object and a surface are given.

### 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.

**Sliding and Stuttering**

Students use a spring scale to drag an object such as a ceramic coffee cup along a table top or the floor. The spring scale allows them to measure the frictional force that exists between the moving cup and the surface it slides on.

**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...

**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 ...

###
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

- 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?
- Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (Grade 6) Details... View more aligned curriculum... Do you agree with this alignment?
- Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. (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?
- Recognize and represent proportional relationships between quantities. (Grade 7) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve linear equations in one variable. (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?

###### State Standards

###### North Carolina - Math

- Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. (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?
- Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (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?
- Recognize and represent proportional relationships between quantities. (Grade 7 ) Details... View more aligned curriculum... Do you agree with this alignment?
- Solve linear equations in one variable. (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 student; 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 (have students bring these from home or purchased 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
- several standard weight sets, ranging from 50 - 200 g; alternatively, use large metal washers tied together in groups to make up weights of ~50, 100 and 200 g or plastic bags filled with pennies, sand, gravel, nails or similar objects; two groups of students can share a set of weights, if necessary

### Introduction/Motivation

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

Remind the students, however, about the importance of controlling variables in scientific experiments. In this case, weight is the only variable that differs 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, must be controlled, that is, not varied during the experiment.

Also, point out that since weight is the subject of the experiment, it is the total weight of the object being dragged that is important. If students start with an empty coffee mug, its weight is not zero, but rather the weight of the mug itself. (This is easily determined by hanging the mug from the spring scale.) Then, each time they add weight to the mug, the new total weight is the weight of the mug plus whatever additional weight was placed in the mug. Show students the weight sets that are available for them to use, and then let them proceed with planning and executing their experiments.

### 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 will still need to make several decisions in order to design an experiment to test for the effects of weight on friction. Write the following list of questions on the board (or provide them in a handout):

- How much additional weight will you use? Will you test just one additional weight, or several different weights?
- 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 is ready to conduct its experiment.

Part 2: Conducting the Experiment

Provide student groups with the materials, and direct them conduct their experiments.

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 of the associated lesson. Then ask them to write a paragraph describing what their data show about how weight affects friction.

### Troubleshooting Tips

As necessary, remind students that spring scales have a limit to how much force they can measure (scales with a 500 g limit are recommended for this activity). If they put too much additional weight in their mugs, the frictional forces may exceed the spring scale capacity and could even damage them. Expect them to be able to obtain reliable results for their weight experiments using added weight between 50 and 250 grams.

### Investigating Questions

As students design their experiments, ask questions such as:

- Why is it a good idea to conduct multiple trials of an experiment? (Answer: Multiple trials let us see if we get consistent results, which can indicate whether or not our experimental design and/or measurement methods are appropriate. They can also let us know if a measurement error might have occurred, if we get one result that is very different from the others.)
- Why is it a good idea to test several different weights, instead of just adding one amount of weight and comparing its friction to that of the empty cup? (Answer: Since it is not yet known what the effect of weight will be, by testing several different weights we can see if there is a consistent trend based on the amount of weight added.)
- 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 weight varies, we don't know if weight will affect both static and kinetic friction, or just one, or neither. Measuring both gives us a more complete picture of how weight affects friction.)

As students conduct their experiments, ask questions such as:

- Based on what you are seeing so far, what effect does weight seem to have on friction?
- Based on what you already know about friction and what causes it, why do you think adding weight 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 (weight) on the x-axis. Make sure that their graphs also include the origin (0,0), axes labels (including units), and a legend if both the static and kinetic friction are shown in one graph. Have students analyze their graphs and determine the relationship between the friction force and the weight. Specifically discuss in terms of how the dependent variable changes when the independent variable changes.

### Contributors

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

© 2014 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://ciblearning.org/ for information about CIBL and other resources for K-12 science and math teachers.

Last modified: January 10, 2019

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