I covered my colleague's honors physics class this morning while he was at a track meet. (Yes, we have Saturday classes.) The students were correcting their incorrect answers to a recent test.
One question was the classic about two carts of unequal mass at the top of a smooth incline -- which has more speed at the bottom? Several people initially couldn't understand why their instinct wasn't right, whether that instinct was that the heavier cart or the lighter cart should be faster.
I gave my standard advice -- forget your instinct, start from first principles, write out the full conservation of energy equations for each cart. Sure enough, everyone quickly solved to see that mass doesn't appear in the equation for speed at the bottom, so that both carts should move with the same speed.
But I could read faces. They did NOT believe in physics. I asked* if anyone would be willing to bet, say, $100 that a heavy cart would beat a light cart to the bottom of an incline, or vice versa. They initially said "yes," then looked at my face. "Well, no, 'cause you would win, wouldn't you."
*facetiously, of course, and always in the subjunctive mood... too bad, though, because I could make SO much money gambling on physics.
Of course I'd win. But I don't want to win the argument with a thought experiment, or via my status as the teacher. I want to win the argument with an actual demonstration of the right answer.
So I quickly grabbed two PASCO carts, sticking some extra mass on one of them -- you can see the setup in the picture. I elevated one side of my PASCO track, which is pretty danged close to being frictionless. I let the carts go... they reached the bottom at the same time. Physics works.
"Now, do you believe?" I asked. To his credit, one student said no: "Switch the carts, please. Put the heavy cart in front of the light one." Great point. Not that the switch changed the answer, but he did a good job asking a key question.
Anyway, everyone was glad that they didn't bet with me, even figuratively. They can try to argue with math, but students have a really hard time arguing with an experiment that's performed right in front of them.