Salami Forces

There is a problem in my 10th edition of Halliday, Resnick & Walker that asks students to determine the force read by the spring scale in this image:

Prior to trying this problem, students are asked to complete this desmos card sort, originally written by Brian Frank. I asked students to complete it individually, without collaboration, which is hard for them. I tell them that I'm not grading it for accuracy. Then students attempt this textbook problem in groups. The salami in the problem is 11 kg, which I start the discussion by putting in context for them. We joke its more like a holiday ham than a salami. 

As we review the problem, students have no problem agreeing the scale reads 110 N (when g is 10 m/s^2) in the image (a) and (b) but start to disagree with their answers for (c). I ask students to raise their hands to vote if they think the spring scale will read 0 N (the misconception that the forces balance and therefore the scale reads 0 N), 110 N (the weight of one salami) or 220 N (the weight of two salami). The class is always split so then we get to the "big reveal."

I have some equipment set-ups hidden around the room for this so they don't see it coming. I tell the students we will just have to test it and pull a dry salami from the grocery store out from underneath my desk. I say "Unfortunately our budget constraints mean it is not a 11 kg salami but it will have to do." I hang the single salami from a binder clip attached to a spring scale and it is just about 3 N. Then I go across the room to my "wall" for the next station. 

Going on two decades ago a student completed a project that included two wood boards attached together at a right angle. It has an eye hook on the vertical peice and has been a "wall" for many a demonstrations. A spring scale is already attached to the eye hook on the wall with a string run over a pulley clamp at the edge. I attach the salami and ask a nearby student to read the spring scale. When they confirm its 3 N again I disconnect the salami and I'm walking about to grab the other one I've hidden when I say "That's easy, we all agreed on that. But what about ..." (other salami revealed with flourish) "the second salami!" 

You would this at this point think that students would be expecting it. You'd be wrong. 

I walk over to another set-up which they often haven't noticed. I use a wooden plane or a wide wooden board with two pulley clamps on it. It's helpful to have the board raised up since the salami are long-ish and will hang down. This year my classes are full, even by California standards, so I had it propped up on paper towel rolls (higher than my lab jacks and lighter than a stack of textbooks). 

Also, set-up the pulleys so that the string and scale between them hang horizontally. I have the string, scale and binder clips already there so I just have to attach the salami. A nearby student helps since I can only reach one salami at a time and they get to be the one to reveal the answer. Even when they triumphantly shout "3 newtons!" there is often disbelief and students will come check for themselves. 

After they settle down, I tell them I'm going to say something to help them understand but it will sound silly: "One salami is the other salami's wall." It's like I'm imparting sage wisdom and several students will nod knowingly. 

From there I unhook the salami and start to move to the final set-up. I have a single pulley at the top of one of my tall ring stands with the string already on it. There are two ways I've done this part. I used to just hang the two salami from either end but before releasing ask students what will happen. I purposely hold them so that one is above the other, some think that it will then accelerate down. Most students recognized that the system would remain at rest since they were equivalent in mass. One year, a student asked what the tension was in the string in that case. I said "Let's find out," and then I added a spring scale on the string. Students by this time guess correctly that it will read 3  N. But now the system accelerates, so I ask students why and some of them realize the added mass on one side of the scale makes it unbalanced. 

This activity doesn't take long but has a big pay off for engagement. When I see former students this time of year and they ask me how this year's class is going I can tell them, "They just did the salami problem yesterday" and they get excited. "I remember that one!" It makes this classic tension problem memorable, with the added bonus of being delicious.