I was so excited to try this, I've thought about doing it for years but seemed to never have the time. My AP C students do an Atwood's Machine lab that I've adapted over the years. The original lab came from my predecessor who had students use two identical hanging masses and one small mass. I've been using 200 grams for the "identical masses" and a 20 gram mass as the small one. The students used a known fall height and stopwatch to determine the acceleration with the small mass on one of the larger masses and then with the other in case the two identical masses weren't actually the same. They used a smart pulley with a Vernier photogate so the second part of the lab asks them to find the slope of the velocity-time graph as another way of finding the acceleration. The second day challenged students to find the mass of one penny using the same method. Instead of the small mass, students used a stack of four pennies (being sure to have them all before or after 1982 when the mass changed).
After trying the lab this way for a few years, I cut the second part of applying the same method to find the mass of the penny. I always liked the challenge aspect but not the fact that students essentially did the same lab twice. For years I wanted to challenge them to find the mass of some random object that was attached to the pulley set-up instead. And this year I made it happen.
First stop was the local dollar store. I bought a wide variety of objects, figuring that I could then see what worked and what didn't. I got plastic models of insects and whales, knock off My Little Pony's, small knot balls cat toys, dryer balls, rubber duckies and more. The next step was to pair them up, add eye hooks and fill one of them with additional weight.
Some pairings were easy, like a rubber ducky version of Elsa and Olaff from Frozen. Each got a tea cup hook attached to their top (glued in for extra security). The ponies were the easiest to add mass to because I could pull off the head (a separate piece so it could rotate) and put the lead shot in with a spoon.
Others, like the dog toys shaped like candy and the rubber duckies already had a hole in the bottom larger than the lead shot. I poked a small hole in the bottom of a styrofoam cup to act as a funnel. I found the best method was to only partially fill the bottom of the cup. Then I shook the cup a bit and let a ball bearing or two find the hole, kind of like playing those 3 D marble maze games. So I walked around class shaking this cup on top of toys while I helped students with day one of the lab.
Some objects had either a hole that was just the size of the individual pieces or had no hole. In the case of the dryer ball, I had to fill it one piece at a time with some tweezers. Now I didn't fill the ball. I massed the two objects that would be paired to see if they were the same. If one was heavier that was the one that I added lead shot to. I wanted a difference in mass of at least 20 g, I made it larger for larger mass objects. I wanted the differences in mass to vary from pair to pair so it wasn't the same for group to group.
After the object was filled, it had to get sealed up so the lead shot I had painfully added didn't fall out. In the case of the dryer balls the hole was about the size of the tea cup hook I added so with a bit of glue that was easy enough. In the case of the whale and shark figures that didn't have a hole to begin with, I drilled a hole into one of the eyes. To help add weight, I used very short nails with large nail heads to seal those holes.
The rubber duckies, that had a convenient when filling hole in the bottom, now needed that hole securely filled. I cut up small pieces of flat toothpicks and filled the hole which then also got sealed in glue. Once the glue was dry I used wire cutters to trim sticks. I would have love to use a small dowel but didn't have any wood chopsticks with me (which I suspect would be just the right size).
The models of insects turned out to be solid. I even needed a pair of pliers to twist the tea cup hooks into them. I didn't see an easy way to securely add mass to one of the two pairs internally so I just looped some washers onto a zip tie and gave the one destined to be heavier in each pair an accessory.
There was a set of Paw Patrol figures that I tried another method with. I stuck a nail through the bottom of one figure, through its top and into the bottom of the second so it was stack of two. Being the same size as the third in the set, they were now heavier than the one by itself (plus the weight of the nail). I also already had some large figurines of animals of Australia and some cockatoos I had from another lab that I could loop the string around if I didn't want to add the tea cup hook to. I also picked up a slotted and solid spoon, that I added a ziptie of washers to in order to make the mass difference larger.
In the end, I ended up with quite the assortment of nearly 50 objects:
It wasn't quite enough for a unique pair of objects for each of the 9 lab groups across 3 periods of AP but it's getting there.
So today was the day to try the lab practical out for the first time. I made a simple sheet that explained to students they had to find the difference in the mass of the two objects. I gave them a similar table of 6 trials that they had in the original lab. They could use either method (timing a known distance or acceleration from a v-t graph using the LabQuest) but had to show me their method on the paper.
As the first period started the lab, I realized they should have the combined mass of the two objects or would find the difference between them in terms of "total mass." I walked around with the balance and groups were able to record the combined mass of the two objects but not the individual masses. Once groups collected data and made their prediction I came back with the balance to mass the objects individually. Most groups got very good data, less than 10% off of the measured value of the difference in mass. Those that did have larger error found their initial derived equation was flawed and they were able to try again.
There were several groups that predicted the mass of each individual object as well. I need to take a closer look at their work and see if their work is valid. A few groups took the instructions of "similar objects" to mean that they were identical so I don't know if they just assumed each was half the size of the combined mass. Some of the pairs did start out as identical before modification but several had difference of a few grams.
Overall I loved it. The kids thought it was fun and were able to prove that they could successfully apply the same method to a different scenario. There were a few issues with the weight and shape of some objects, some issues were like any other Atwood's lab. If the masses are too heavy they can pop the smart pulley off its point connection. If the objects hit the ground the slack in the rope can cause the string to fall off the pulley. Pushing the objects up or down instead of dropping them from rest can affect the data. Groups wanted to use the same fall distance they had before, when their smaller cylindrical weights could pass by each other more easily, and found the larger objects couldn't do that.
I'm excited to continue to collect random objects for this lab and to do it in the future.
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