Lesson: Factors Affecting FrictionContributed by: Engineering K-Ph.D. Program, Pratt School of Engineering, Duke University
Educational Standards :
Pre-Req Knowledge (Return to Contents)
Learning Objectives (Return to Contents)
Introduction/Motivation (Return to Contents)
In the previous lesson (Discovering Friction) and its Associated Activity (Sliding and Stuttering), students found that friction is a force that impedes motion, and that static friction is greater than kinetic friction. They also found that surface roughness can be an important source of friction, but their experiments should have revealed that a lot of friction could also occur between two very smooth surfaces. The discussion following their experiments should also have raised questions about the roles of weight and contact area in the amount of friction that occurs between two surfaces. To introduce this lesson, remind students of these observations and questions from the previous lesson.
Then, ask them to meet in their groups and formulate two hypotheses. The first hypothesis should state what they think the effect of adding weight to the cup will have as it slides across a surface. Example of such hypotheses might be, "When more weight is added to the cup, more friction will be measured when we slide it across the table," or, "Weight will not affect the friction measured." Ask students also to write the reasoning behind their hypotheses. For the first example, students might say, "We think we will measure more friction because the extra weight will make the cup press down on the surface more, so more of the tiny surface bumps will be in contact." For the second example, students might argue that, "Weight will not affect the amount of friction because the same amount of surface on the bottom of the cup will be in contact with the table's surface. We think that to get more friction, there has to be more surface area in contact."
The second hypothesis each group should make concerns the effect of contact area on the friction measured. Students will probably suggest that, "The more surface area in contact, the more friction we will measure." Their reasoning will most likely be along the lines of, "The more surface area in contact, the more tiny bumps there are to get in each other's way between the two surfaces." Or, if they are familiar with the notion of friction due to molecular attraction, they might also argue that, "The more surface area there is in contact, the more places there are for molecules of the two surfaces to be attracted to each other."
At this point, you need not discuss their hypotheses or their reasoning. However, do check to see that the explanations they give for their hypotheses are reasonably complete.
Once the groups have formulated their hypotheses and explained their reasoning (in writing), let them know that they will be able to test their hypotheses using the same basic method they used in the previous lesson.
Lesson Background & Concepts for Teachers (Return to Contents)
The effects of weight and contact area on friction are complicated because there are two major mechanisms of friction at work. The classical view of friction is that it is caused solely by surface irregularities, called "asperities", and that weight correlates directly with the amount of friction that occurs. For a single object moving across a single surface, when additional weight is added to the object, the frictional force measured is in direct proportion to its total weight. A graph of the friction measured versus the total weight will produce a reasonably straight line such as the one drawn from student data shown below . This will be true for both static and kinetic friction, although the line for static friction should be a little steeper than the line for kinetic friction.
The slope of the line corresponds to the coefficient of friction for the two particular surfaces involved. In physics and engineering, the coefficient of friction is denoted by the Greek letter mu (μ), followed by either the subscript s or k. Thus, μs and μk represent the coefficients for static and kinetic friction, respectively. The force F needed to overcome friction and set a body of weight W in motion on a flat surface is given by F = μsW. Likewise, once the body is in motion, the force needed to keep it in motion is F = μkW.
Every pair of surfaces has a unique, empirically obtained set of coefficients. For example, dry steel on dry steel has a static coefficient of about 0.6 and a kinetic coefficient of 0.4. When oil or grease is added, the coefficients drop to about 0.1 and 0.05, respectively. These coefficients were obtained by measuring the force needed to move an object made of steel resting on a flat steel surface, and then dividing that force by the weight of the steel object. In other words, the equation given above was rearranged to give μ = F/W.
The table below lists some examples of coefficients of friction. Since it is mainly engineers who use these values, most of the ones found in reference materials are related to machinery and automotive applications.
Since the frictional force measured varies in direct proportion to the weight of the object being moved, there must be some physical mechanism underlying this observation. Given that this friction is due to surface irregularities, it makes sense that additional weight presses the peaks and valleys of one surface more firmly into the valleys and peaks of the other surface, so more force is required to disengage them and set the body in motion. Similarly, more force is required to keep the body in motion when gravity acting on the added weight tends to re-engage the peaks and valleys.
But what about contact area? How does it affect friction? Returning to the equations for friction given above, F = μsW and F = μkW, we can see that friction only depends on the weight of the object being moved and the coefficient of friction that exists between the two surfaces. The amount of surface area in contact does not appear in the equations anywhere. So, the amount of area in contact doesn't seem to matter when it comes to friction.
This might not seem to make sense at first. However, consider that as long as there are some surface imperfections present on one or both surfaces, friction will occur. And as long as a few peaks and valleys are getting hung up on each other, it makes no difference if other peaks and valleys are also getting hung up simultaneously as long as these additional peaks and valleys aren't bigger than the original set of some peaks and valleys. The force required to free up any number of peaks and valleys is the force needed to free up the largest of the peaks and valleys. No matter how many smaller peaks and valleys there are, the larger force is enough to free up all of them. The coefficient of friction between two surfaces, because it is empirically derived and based on numerous experiments, reflects the largest peaks and valleys typical of the two surfaces involved. So, as long as the surfaces are relatively uniform, meaning they don't change in microscopic texture from one region to another, the amount of area in contact doesn't affect the frictional force.
At least that's the theory, and in fact, it holds true for the classical type of friction, sometimes known as "normal" friction, that is the result of surface roughness. However, in the last several decades a whole new class of very smooth, lightweight, synthetic materials have been invented and manufactured for a variety of applications. And while they may be very smooth, even on a microscopic level, some of these modern materials (mostly plastics) show an astonishing amount of friction. For these materials, the classic view of friction does not apply in its entirety. Although the amount of friction measured can still be affected by weight, friction due to molecular attractions between the two surfaces appears to be just as important. For these materials, the amount of friction that occurs can, in fact, be affected by the amount of surface area in contact, although at this point the nature of the molecular attractions involved is poorly understood. An example of a graph created from student data showing the effects of contact area on friction between two smooth, synthetic surfaces is shown below.
Vocabulary/Definitions (Return to Contents)
Associated Activities (Return to Contents)
Lesson Closure (Return to Contents)
Also, have students calculate the coefficients of friction between surfaces they tested using the method explained in the Lesson Background & Concepts for Teachers section above. Show students a copy of the coefficients of friction table included in this section for comparison. Be sure to point out how the coefficient of friction between a car's tires and the pavement is reduced when the pavement is wet; this is why safe drivers slow down on wet roads to avoid skidding. Advise your students to remember this fact after they get their driving licenses!
Students may find some of the other friction coefficients surprising, such as the comparison between glass and diamond. Ask your students to speculate on why these two materials, which are similar in appearance, have such different coefficients of friction. They might want to do a little library research in an effort to find out why. They should easily be able to find information about what these materials are made of, but it is unlikely they will be able to find out much about how they behave with respect to friction. Point out to students that many aspects of friction are still poorly understood and are being researched by scientists and engineers throughout the world. Nevertheless, the similarities and differences between glass and diamond are such that students should be able to come up with some plausible explanations, or hypotheses, especially since they are armed with knowledge about the importance of molecular attractions in smooth-surface friction.
Assessment (Return to Contents)
Lesson Extension Activities (Return to Contents)
Rolling friction is another type of friction, and it is generally much lower than the sliding friction students experimented with in this and the previous lesson. Students can conduct additional research, both in the form of library/internet research and experimental research, to learn about this type of friction.
Other Related Information (Return to Contents)
This lesson and its associated activities were originally published, in modified form, by Duke University's Center for Inquiry Based Learning (CIBL). Please visit the website http://www.biology.duke.edu/cibl for information about CIBL and other resources for K-12 science and math teachers.
ContributorsMary R. Hebrank, Project Writer and Consultant, Pratt School of Engineering, Duke University
Copyright© 2004 by Engineering K-Ph.D. Program, Pratt School of Engineering, Duke University
including copyrighted works from other educational institutions and/or U.S. government agencies; all rights reserved.
Supporting Program (Return to Contents)Engineering K-Ph.D. Program, Pratt School of Engineering, Duke University
Last Modified: April 18, 2014