Captured Thought: Physics

Recently, I haven't had any "Oh, NOW I get it" moments. Nothing really awesomely pertinent, important, and insightful has given me this kind of feeling. The closest thing to this feeling that I got recently was when I was taking a physics test.

The question was that if there was a 64 newton force applied to the first of two barrels, which weighed 13 ad 6 kgs, respectively, how much tension was in the chord connecting the two barrels if the coefficient of friction for the barrels was .329. Basically the way we had been taught to do it was to find the acceleration of the entire body as a whole, and since the acceleration would be the same for both the first and second barrels, we could take the acceleration and multiply it by the mass to get the net force. Then we could calculate the force of friction (.329 * 6 * 9.8 for the smaller barrel) and add that to the net force to get the forward force of tension. During the test, I started playing with variables and started cancelling terms out. I realized that there was a much easier way to do this that our teacher hadn't taught us; we could take the ratio of the mass of one of the barrels to the combined masses and multiply that by the applied force to get the applied force on each barrel. So basically, I confirmed for myself WHY this type of problem works the way it does.