A “New” Way of Solving a Physics Question

I have been teaching physics for a while now (this is year 22 for me not counting teaching while still in college). Over those years I have given the following question on and off pretty regularly.

“Captain Bialar Crais has a mass of 81-kg, and he has been captures in a secret laboratory. He wants to escape from a third-story window. Unfortunately, a very long makeshift rope made of sheets tied together can only support a mass of only 45 kg. How might Crais use this “rope” to escape? Give quantitative answer as well as a qualitative answer.”

(Yes, I used a name from the show Farscape for this question – I love that show).

This is in a section on forces. They have learned about Newton’s three laws of motion, and the basic motion equations. They have learned about free body diagrams and Fnet equation.

My expectation on answering this question was always that students would say the Crais could double up the “rope” and then have basically two ropes and each could suppose half his mass and he can descend down the ropes safely. In the 22 years of giving this question that is always how students have answered this question (if they answer it correctly). There are always some students that say it can’t be done since the rope can’t support his mass.

That is until this semester. As a reminder, I am teaching an asynchronous physics class for the first time. That means I never meet with the students. The students do everything online on their own time, and I grade it. They have weekly modules that have due dates and they have to turn stuff in on. Of the 29 students that turned in this question all but a few answered it in the following way (to some degree of wording):

“He creates a downward force of 793.8N due to his weight. The rope can only support 441N of weight. So, Crais must create an acceleration to reduce his mass. So, you subtract the two number: 793.8-441 = 352.8N, and that is the force he needs to create to slow himself down. This is done with friction between his hands and the rope. That means he has an acceleration of a = 352.8/81 = 4.36m/s^2.”

I was a bit dumbstruck by this answer. I thought, it seems right, but it doesn’t seem right. And I was like, “Where did this answer come from?”

After some thought I realized that this answer does work, but not the way most of the students were phrasing their answers. Most were saying that the above acceleration was the maximum acceleration he could have, and that is wrong. That was the minimum acceleration he could have. Because if he didn’t use the rope at all then he would accelerate at 9.81m/s^2 (go gravity!). But the students weren’t saying he needed at least 4.36m/s^2 of acceleration they were saying he couldn’t exceed that acceleration or the rope would break.

So that made me wonder where they answer came from.

So I turned to the internet and typed in my question – and you guessed it, it was solved in that manner online (slightly different wording and no Crais, but the same question). And sure enough whoever solved it online did it in the above manner.

So, while the answer is quite clever and I liked it it was clearly copied off the internet by most of my class. That was a big disappointment, but regretfully not a surprise for a few reasons:

1. It is the world we live in right now. And there isn’t really anything I can do but give 0 when I catch it and can prove it.
2. On the same homework assignment the same group of students (mostly) had done another question using energy conservation and not forces. For you physics teachers out there we haven’t covered energy conservation yet and having even talked about it yet. So, they fact that they had all done it that way raised another big flag, and sure enough Chegg had it worked out the energy way.

When I called students out on it (as a whole, not individually). I had 1 student fess up and be honest with me and apologize (which was nice). I had a few students email me and say, “I learned about energy in another class and used that” (I find that somewhat hard to believe).

I had to make clear to the class that homework assignments are there for the students to show a teacher that they can apply the material being covered in a section to applications being asked about. The questions aren’t there just to be answered. I want to know that they can use the material effectively. While they did that in the first question mentioned above they didn’t understand the meaning of their answer, and as a result didn’t get why I was asking the question. The second question they clearly just wanted to get an answer and move on.

I actually like the way the students answered the Crais question. I had never thought of it that way, and I am not sure why. I think that answering it that way and then understanding that to maintain any kind of acceleration dow na rope would be VERY hard to do, and therefore doubling up the rope would be a much better and safer option. So, maybe I will reword the question in the future and incorporate both ways into it.