I will admit, I love
analogies. I find them useful when others are explaining things to me and I use
them naturally when I am explaining things to students. I also recognize that
not everyone feels the same way.

Many studies have been done on the usefulness of various analogies when teaching about electricity. Is electricity like water or air or a crowd of people, are wires like a tube or a hallway? Analogies don't have to be perfect to be useful. Sometimes identifying ways that the analogy fails and the two things are not alike helps students understand better.

Today, we were talking about voltage. The book described the action of the battery as being similar to a pump lifting water up high so that it would fall down through the circuit. This analogy works great for energy ideas and even current, but not really for voltage. We decided to see if there was a measurement in a gravitational system that was analogous to (like) voltage in an electrical system.

It was interesting to listen to the students as they worked through things they knew looking for the best fit. This is a summary of their discussion.

Questions: What measurement in a gravitational system is like voltage in an electrical system.

Many studies have been done on the usefulness of various analogies when teaching about electricity. Is electricity like water or air or a crowd of people, are wires like a tube or a hallway? Analogies don't have to be perfect to be useful. Sometimes identifying ways that the analogy fails and the two things are not alike helps students understand better.

Today, we were talking about voltage. The book described the action of the battery as being similar to a pump lifting water up high so that it would fall down through the circuit. This analogy works great for energy ideas and even current, but not really for voltage. We decided to see if there was a measurement in a gravitational system that was analogous to (like) voltage in an electrical system.

It was interesting to listen to the students as they worked through things they knew looking for the best fit. This is a summary of their discussion.

Questions: What measurement in a gravitational system is like voltage in an electrical system.

After a few attempts, this is what the students can up with. (Yesterday, I accidentally loaded one of the incorrect student solutions. Sorry about that.)

This was really a breakthrough for the students. They saw that there was a fundamental difference between the two systems that was making an analogy difficult. In an electrical system, the force acts on charge, but the effect of the force depends upon mass. So both quantities remained in the equation. In a gravitational system the force acts on mass and the effect of the force also depends upon mass! So the mass cancels out.

The unknown analogous quantity is acceleration times distance. We don't really have a name for that. (I think it reduces to one over time squared.)

When we studied mechanics, I told them that remarkably mass was a measure of an object's inertia

__and__a measure of the force that gravity would exert on it. They sort of nodded but were pretty unimpressed. But after working through this analogy, they had a greater appreciation for this distinction.

The next question they asked me, of course, was why. I told them that I did not know. But I was able to quote Eric M. Rogers. "The physicist who does not enjoy watching a dime and a quarter drop together has no heart."

Comments?

I'll condense a comment that didn't post yesterday. Analogies are always good to link the familiar to the unfamiliar … until they don't. When that happens, we've learned something.

ReplyDeleteWater is a good analogy to charge flow (but not the best one) and I've used it to prove a point about the speed of charge flow. My students know where the city wells are and can estimate the distance from the school. I give stopwatches to a couple students and have them time how long it takes from me turning a faucet and getting water. I ask how fast the water needed to move.

They get that the water was already in the pipes and then need not consider charge moving from the battery or power station. Capacitors and island circuits convinced the rest of the skeptics.

Water does not work well to explain the use of capacitors in so many circuits today. That was the reason for the C in CASTLE.