Torque Sticks

During our unit on torque and center of mass students hang meter sticks from ring stands to find their center of mass. But these meter sticks have one end wrapped in lead solder so that the center of mass is not at 50 cm. Students hang the meter stick from a fulcrum they could shift and added weights to the other side of the meter stick until it was level. They complete at least three trials to determine the unseen center of mass.

 While this moves the center of mass considerably I have two problems with it:
1. I was a little concerned about exposed lead solder so I wrapped each hunk with electrical tape. Once I put the solder piece on students were not to move it. Sometimes students listen, sometimes they don't.
2. Students did not think about the lead solder as part of the meter stick, as if it had a heterogeneous mass distribution. They thought of the mass as an added weight and when drawing force vector diagrams might label an applied force at that point. Or students would draw the Force of Gravity of the entire meter stick as coming from this point, not from the center of mass.

I bought sticks that were very similar to meter sticks but not quite the right height. I planed them down a bit so that they fit the meter stick holders I have. Then I drilled lots of holes into them.

I tested one stick and found that drilling holes on one side only shifted the center of mass about half an inch. I needed to add more mass to one side or remove more mass from the other. I decided to add melted lead solder into each hole. I put tape behind the holes on one side of the stick and then used a soldering gun and iron to melt the 50-50 lead solder into each hole.

 

One of the trickiest parts was trying to keep the puddles of solder below the top of the hole. Its not a big deal if it bulges over but the next tape step is easier if its level. 

I had one stick that was my sample stick, for instance now I know not to try a spade bit as it will crack the wood. On this sample stick six or so lead filled holes on one side of the stick shifted the center of mass considerably. In the bottom right you can see the original center of mass point with empty holes marked beneath the pen and the new location of the center of mass once they were filled with lead shifted to the left a few inches.

So I had a lot of holes to fill with lead. It took almost two hours to fill 184 holes on these sticks.  Every stick has holes on one side (left picture), some of them also had empty holes on the other side (right picture). The majority of the weight shift is due to the lead but taking a bit of wood out of the other side helps a bit. Each stick has a different amount of holes so that the center of mass will be different.

The lead filled hole side got another piece of masking tape covering the lead. This helps with the illusion that the stick is homogeneous even when its not. And it will help protect students from the lead. I looked up the hazards of lead solder and the main issue seems to be ingesting lead dust from your hands after working with it. Washing your hands after working with it seems to make it perfectly safe. 

I plan on using these sticks as part of a lab practical. Students will have to balance the sticks with a set fulcrum position. I can nail the hanger that acts as a fulcrum into one position so that students can't move it. They will conduct a few trials with different masses on the other side (empty/ no hole side) in order to calculate the position of the center of mass. By labeling each stick and keeping a key I will be able to check my student's work. I'm hoping these new sticks will prevent some of the misconceptions involved with this lab.