Yesterday was a very busy day. It started with Physics class, a quick lunch, then 2 hours in the lapidary shop, polishing rocks, swim class and then a special lecture by UC Berkeley Professor Alex Filipennko on black holes. The black hole lecture actually complimented our physics class and big history class quite nicely.
Unfortunately the physics lab didn’t go as planned today, at least it took more time than I thought it would so we didn’t quite finish. The students are going to be graphing their data at home this week and we’l analyze the results next week. I started the class with a flying bat toy hanging in my tree in the front yard. It has batteries and if you give it a push it will fly, wings flapping and everything, in a nice little circle. I asked the kids to use the video physics app to record the motion, either from the side, or from directly below the bat and see what they get. The black bat with a complicated tree pattern as the background made automatic tracking freak out so the kids had to mark each point by hand in the video but they got some really nice results. The graphs below were done by recording the motion of the bat from below and marking the origin as the center of the circle. As expected they got beautiful sine and cosine curves for the motion and you can easily read the period of the motion, when it starts to repeat, off the graph as 1.5 seconds.
Once they finished looking at their graphs we went inside and talked about circular motion a bit before starting the next lab. I asked the class if the bat circling in the tree was accelerating and they said no because the speed is constant, so I reminded them that acceleration is a vector and has direction and so does velocity. So the speed may be constant, but the direction of the bat is constantly changing so its constantly accelerating towards the center of the circle and we call this centripetal (center seeking) acceleration, which is caused by a centripetal force – the string in this case. To see how the speed of the object depends on the radius of the circle, we did an experiment where we could exert a constant centripetal force by hanging a know mass (100g) on the bottom a string which passes through a tube (empty bic pen) and is then tied to a rubber stopper (the object that is going to be experiencing uniform circular motion).
You can see a student swinging the rubber stop in the photo, and the brass hanger with 100g at the end of the string. Once the student has the stopper moving uniformly and quickly enough they can let go of the string and just hold the tube. Then their lab partner measures the time it takes for the stopper to make 10 revolutions. The lab we did was very similar to one I found on the University of Wisconsin website (the link went bad and I can’t find the lab there anymore so I removed it). The students marked the radius they wanted by placing a piece of tape on the string below the tube. This way they could spin the stopper until they got the tape in the right place and know they had a certain radius. They were to do this for 4 or 5 different lengths and then make a graph of speed squared versus the radius and find that its a straight line. I think one of the pen tubes we used was causing too much friction, at one point the string broke and sent the rubber stopper flying! Luckily we were doing this experiment outside and no one got hit. I’l have to wait and see how their data looks but I’m thinking we may redo this lab with better tubes and fishing line instead of string. It would also be nice to measure the speed of the motion as a function of the centripetal force by changing the mass hanging off the bottom of the string.
After lunch 5 of the kids went with me to the local lapidary shop to grind and polish rocks. This is a hobby my son and I got into through 4-H. We joined the local rock club so we could use the shop more often and this summer I became a foreman so we could open the shop during the afternoon for homeschool teens. Its a great hobby for teens and it involves quite a bit of patience and skill, not to mention they get use to cutting and grinding wheels. Here’s a tiger eye cabochon that my son made last year. We’ve learned how to wire wrap and actually make most of our christmas gifts now. So if your teen is looking for a cool hobby you might contact your local rock club and see if they have a shop or offer classes.
The last event yesterday was a lecture on black holes at the local theater. I was very impressed with the talk by with Alex Filippenko, he’s a great speaker and when it came time for Q&A, he made a special effort to take the kids’ questions first. In his talk, he explained how we know, or at least are confident, that black holes exist. Since we can’t see them directly, we have to look for stars that seem to be orbiting a large mass that we can’t see – basically you look for circular motion (well elliptical motion) of a star and from measuring the doppler effect (red shift and blue shift when its moving away and toward us) of the spectrum emitted you can determine the period of the motion and the mass that must be causing it. So basically he does what the kids did in class with the bat and the stopper – find the period of the motion and from that determine the force causing the motion. Filippenko has co-written an introductory Astronomy textbook and he’s done a couple of Great Courses, one of which is available through the Great Courses Plus beta which ends unfortunately, this weekend. I’m still debating whether or not we’l subscribe to that service. Its going to work like Netflix, pay a monthly or yearly fee and have access to a huge number of Great Courses. Our biggest problem is finding the time to watch them and of course it depend on the price of the subscription. If you have a kid interested in Astronomy I would definitely give his Great Courses a look for he’s a lively and entertaining professor.