The set of problems today asked students to draw multiple representations based on given velocity-time graphs, but also to say whether the forces were balanced, unbalanced in the positive direction, or unbalanced in the negative direction.

After the first problem, one student volunteered a rule (I didn’t prompt this!)—that the unbalanced forces were correlated with the acceleration. That 0 acceleration means balanced forces, positive acceleration means positive unbalanced forces, and negative acceleration means negative unbalanced forces. We decided to check each future problem against that rule.

Even though the first rule seemed to work for the next couple of problems, another student proposed (also unprompted!) a competing rule—that positive unbalanced forces mean speeding up and that negative unbalanced forces mean slowing down.

The rules were in direct competition during one of the next problems, and we decided to do an experiment with the human dynamics cart in the hallway to test out the idea. (Of course, I didn’t think to bring my phone out to the hallway to take photos. Oops.) After getting a student rolling in the negative direction, another student pushed her “negatively” to see if negatively unbalanced forces would slow the student down.

After it didn’t work, they tried pushing “positively”, and that did slow her down… and then it stopped her and started her speeding up in the positive direction. We were able to eliminate our second rule, and the updated board was another confirmation of our first rule.

In the last part of class, we talked about how to (usefully) annotate velocity-time graphs so that we could use them to solve problems, and students worked on the final page of the packet. We have one more bit of solving and whiteboarding to do, so we should also be able to move on to unbalanced forces at the start of next week. Go Mechanics!

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