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21 October 2014

Friction coefficient on an object of unknown mass -- lab, homework simulation, or test question

I've been a fan of Phet's "Force and Motion: Basics" simulation for several years now.  It includes several tabs: the "tug of war" which inspired a daily quiz that I'll likely post soon; a "motion" tab that allows you to apply forces and see the speed change, but in animation and in a speedometer; and an "acceleration lab" tab that allows for all sorts of investigations connecting net force, acceleration, mass, and speed.  I'd suggest downloading the java version and playing with it for a while.  In fact, I give extra credit to my students merely for noodling around with this simulation for at least ten minutes one night.

A few weeks ago, I discovered the "friction" tab.  You can see a screen shot above.  By clicking on the "applied force" slider, you cause the stick figure to push on the box in either direction with any amount of force.  The checkboxes in the yellow area allow you to display the net force, the individual forces, the masses of the objects, and a speedometer.  Students can see that pushing the box doesn't cause the box to move immediately in the direction of the push; rather, the box slows down or speeds up based on the direction of the net force.  That analog speedometer does more to bust the misconception of net force being in the direction of velocity than anything I can do or say in class.  

But wait -- there's more.  I clicked the checkbox that says "masses."  As you might expect, the mass of each object is displayed.  You can make the girl sit on the box, and she'll even hold the 200 kg refrigerator without complaint if you make her.  Great.  Students can see how the speed changes more or less rapidly when different masses and forces are involved.

Take a careful look at that wrapped present in the bottom right corner.  Its mass is displayed as a question mark.  Ooh... that seems like an invitation to an open-ended investigation.

My question: determine the coefficient of friction between that present and the surface (with the default setting for the friction slider).  That's not a simple plug-and-chug problem because the mass of the present isn't known -- okay, the simulation displays the value of the friction force, but it doesn't tell you the value of speed or acceleration.  So neither "Fnet = ma" nor "Ff = μFn" gives enough information to solve with a single trial and single equation.

Students are asked to write up their solution in a single page, as if this question were a job audition for their engineering firm.  I have a different teacher or an advanced student rank all the submissions, placing each in one of four categories:

"Hired" (one submission only)
"Recommended to other companies"
"No recommendation"

Hints about using this idea:  For one thing, be sure to open the simulation in java.  I unfortunately had one class open using html5, which is simpler to use and which works on ipads.  But on that version of the simulation, the mass of the present is displayed for all to see.  Oops.

Secondly, there's no reason to stick with this as a pure simulation.  Use wooden blocks, or the PASCO friction apparatus (which is just an open plastic box with a rough bottom surface and a place to attach a string).  Don't allow anyone to measure the mass of the wooden block, but ask them to determine that and the coefficient of kinetic friction using force probes or spring scales only.  The only reason I did this with the simulation rather than as a live, hands-on laboratory exercise is that we had done enough already with that friction apparatus this year.

And finally, this would make a great AP Physics 1 essay-style short answer question:  "In a clear, coherent, paragraph-length response, describe how you would determine the coefficient of kinetic friction between the block and the surface using a spring scale and other known masses."


  1. Hi Greg, I am a 2nd year physics teacher and recently started reading your blog. It is very helpful! Thank you! I like the idea of using the Phet simulation but couldn't quite figure out how to solve for the coefficient of friction if you don't know the mass (unknown present) or the acceleration. Could you post a solution?

  2. I am a big fan of most of the PhET's physics simulations, but there is one thing about this simulation that drives me crazy! As you push the object with a steadily increasing force, it shows the frictional force getting larger also, but at the point where the object starts moving, the frictional force doesn't change. It just stays at whatever it's last value was before the motion started. It should drop slightly due to the transition from static to kinetic friction. Strangely enough, they had no problem illustrating this with the PhET simulation listed right before this one, simply titled "Forces and Motion" without the "Basics." The one good thing about this error is that I can have the students play around with this simulation at home to see if they can "Find the mistake" to really test their understanding of the nature of friction.

  3. Yes... noticed that, too. Drove me a bit batty, too. :-) The simulation still works. I like your "find the mistake" assignment!