A 10 m chain with total mass of 80 kg is laid out on the ground. How much work is required to lift one end of the chain 6 m off the ground?
This is a standard problem from a standard textbook, in the requisite section on work.
Before we solve the problem, we need to draw a picture. So I asked my students to do that the other night.
Can you see the tension?
versus
So. Who’s right?
[vimeo http://vimeo.com/35652114]Surely you object that things would be different if my chain actually weighed 80 kg. Perhaps you are right. Perhaps they would be different.
But here’s the thing…
My 10 ft of chain is a bit more than half a kilogram. So 10 meters of this chain is less than 2 kg. So the chain in the problem is 40 times more massive than the one from my local hardware store. How big is this chain anyway?
Is this inappropriate?
Overthinking my teaching 
Yep, he gets millions of dollars for that book, and can’t be bothered to check whether his numbers are in the sensible range.
But on your first point, I always imagined the chain or rope kind of coiled up in a pile just below where it was lifted from.
Problem reads, laid out on the ground. The physics guy in my department also suggested chain would be coiled. But it’s not.
The point, of course, is that it’s pseudocontext. The values don’t matter because it’s not really a problem about a chain. It’s a problem about a technique. Students aren’t supposed to bring their knowledge about chains to the situation. It’s standard operating procedure in mathematics classrooms.
And it stinks.
I guess my problem is, I have so much more math knowledge than knowledge about chains and things. I’m always trying to make these problems make sense, because I think that’s a good strategy to take. But if you know enough about the real world, then a problem like this does stink.
So. Does anyone use these work techniques to solve real problems? Seems like we should see how a physicist uses this, and then make a ‘toy’ problem that’s easy enough for beginners, but related to the real uses.