Energy Changes due to Friction in a 1st Year Course

[tzonehunter]

I teach a first year Physics course. The incoming students (grades 10-12) have little to no Physics background. We are making some modifications to our work and energy unit. One modification that has been discussed is what to do about kinetic friction. At present, we account for friction as a negative change in mechanical energy by calculating a pseudo-work term (-f_kΔx). We don't look at examples such as a car peeling out from a stop sign. Again, this is a 1st year Physics course...

We have considered changing our accounting of energy changes due to friction as a change in internal energy. For the examples we consider, we would state that ΔE_internal = f_kΔx in the absence of thermal energy transfer in / out of the system. However, should we include the surface in the system as well? Is this getting to be a little too much for the 1st year student?

I'm wondering what all of you do about this.

Thanks.

 

[Stephen Tashi]

According to the Feynman Lectures on Physics, Volume 1, section 12-2 the laws of friction taught in introductory physics courses are not fundamental laws of nature but rather statistical approximations to complicated phenomena that (at the time that writing) are not completely understood.

Problems treating frictional force as a constant are mathematical contrivances that make textbook problems more challenging. There is certainly a tradition in the teaching of mechanics to pose problems that force the student to include dynamic friction as a term in calculating the total force on an object. On the basis that a Physics I course should make students comfortable with the problems traditionally taught in a Physics 2 and subsequent courses, the question becomes whether you should prepare students for textbook problems in future that include friction in accounting for total internal energy. Are such problems as ubiquitous in future courses as the familiar problems of objects sliding down inclined planes with friction etc. that are traditional in a course on mechanics?

 

[tzonehunter]

I scanned through a compendium of old AP Physics B free response problems that addressed Work and Energy. About 50% of those included a portion that required students to calculate or account for energy changes due to sliding friction.

Whether or not it is appropriate to model kinetic friction as a constant force is an interesting debate. Numerous introductory mechanics questions include constant forces exerted over a non-trivial time interval. In reality, this is nearly impossible to observe. For example, we worked on a class demo that involved pulling a low-friction Pasco dynamics cart along an aluminum track using a modified Atwood's setup. We expected to observe a somewhat constant tension force. What we observed was a tension force that changed by +/-20% due to a standing wave set up in the string when the cart was released. We believe this was due to the sudden drop in tension when the cart was released from rest, similar to plucking a guitar string. We were surprised by the degree to which the tension force changed due to this standing wave.

Here's the setup referenced above:
https://drive.google.com/file/d/0Bw3jRUYuv9uwbUIzdzFDanJqVlU/view?usp=sharing

Here's real data from this demonstration:
https://drive.google.com/file/d/0Bw3jRUYuv9uwbDdTdm03VzE0Tm8/view?usp=sharing

 

[vela]

We have considered changing our accounting of energy changes due to friction as a change in internal energy. For the examples we consider, we would state that ΔE_internal = f_kΔx in the absence of thermal energy transfer in / out of the system. However, should we include the surface in the system as well? Is this getting to be a little too much for the 1st year student?

You'd have to include the surface since it absorbs some of the energy and heats up.

The distinction between work and pseudo-work would probably be lost on your students as it's pretty subtle, but I don't think they should have a problem with understanding that the decrease in mechanical energy of the object is balanced by an increase in thermal energy of the object and the surface.

 

[Andy Resnick]

I teach a first year Physics course. The incoming students (grades 10-12) have little to no Physics background. We are making some modifications to our work and energy unit. One modification that has been discussed is what to do about kinetic friction. At present, we account for friction as a negative change in mechanical energy by calculating a pseudo-work term (-f_kΔx). We don't look at examples such as a car peeling out from a stop sign. Again, this is a 1st year Physics course...

We have considered changing our accounting of energy changes due to friction as a change in internal energy. For the examples we consider, we would state that ΔE_internal = f_kΔx in the absence of thermal energy transfer in / out of the system. However, should we include the surface in the system as well? Is this getting to be a little too much for the 1st year student?

I'm wondering what all of you do about this.

Thanks.

Some good comments already, I'll just add that from my perspective, your proposed change introduces significant and largely unnecessary complexity that will require a lot of careful discussion: for example, what exactly is "internal energy"? How do you define the "surface"? What about non-thermal energy transfers? Where does the f_kΔx energy go, if conservation of energy holds?

I recognize the shortcomings of pseudo-work- Arons' book "Teaching Introductory Physics" has some excellent comments regarding teaching friction. One alternate approach is to distinguish between 'active' and 'passive' forces- passive forces are those that adjust themselves is response to active forces (deformation of a spring, deformation of a table when a load is placed on it, friction..), and the passive force cannot increase indefinitely- the spring/table will break, one object will slip over another, etc. A possible example to discuss is pushing a book (or some other object) against a wall- the normal force is then disconnected from weight, and is also easily adjustable. It could be possible to frame the discussion in terms of what range of normal force results in constant motion of the book (or the conditions under which the book remains motionless). Comparing the book/wall system with a low-friction system like wet ice on wet glass may also be useful.

Finally, IMO there's nothing wrong with discussing the fact that there is not yet a full microscopic understanding of the 'cause' of friction (or of any dissipative process), and further, it could be helpful to initiate a discussion about 'dissipation' as it eventually connects to changes of entropy during a process.

 

[scottdave]

You'd have to include the surface since it absorbs some of the energy and heats up.

The distinction between work and pseudo-work would probably be lost on your students as it's pretty subtle, but I don't think they should have a problem with understanding that the decrease in mechanical energy of the object is balanced by an increase in thermal energy of the object and the surface.

This is easily demonstrated by quickly rubbing hands together and feel them get warm, as one example. The harder you press (more force), it will get warmer. Also the more times you rub them (longer distance) it will get warmer as well.