Monday, January 23, 2012
Finding the Mass of a Meter Stick without using a Scale
In order to find the mass of the meter stick without using a scale, I was forced to use my knowledge of physics in order to come up with an answer. First, I figured that I had to balance the meter stick on the edge of the table in order to find its center of mass. Which means that on either side of the center of mass the torques are equal. Then I had to place the weight on one end, which had a mass of 100 grams, and adjust the meter stick to once again find the center of mass. Since I could look on the meter stick and see how long each lever-arm was and i knew the force being applied to the one side I could set up this equation, lever-arm x force = lever-arm x force. I know I can do this because the torques are equal. After I came up with an idea of how to do this I put my thoughts into action. In Step 2 I began by finding the center of mass of the meter stick by balancing it on the edge of the table. The center of mass was at 50.5 cm. Then I placed the 100 gram weight on one side, and then adjusted the meter stick in order to find the new center of mass, which was at 70 cm. The first time I did this process I made a simple mistake. When finding the distance of the lever-arm with the weight, I counted from the center of mass to the end of the stick on the long side. However, all I needed to do was go from the new center of mass to the old center of mass. Which would make the lever-arm of the unweighted side 20 cm instead of 70 cm. This made a huge difference in my calculations. So, after I figured out my mistake the equation looked like (20xforce=30x9.8). The 20 comes from the process I explained above, and the 30 comes from the second center of mass to the end of the stick (weighted side), these are the two lever-arms for the equation. Finally, I got the 9.8 by finding the weight of the 100 gram weight by using the equation w=mg, and this is the force for the weighted side so all that is left to do is find the force on the unweighted side and convert it back to grams. After I completed all of the calculations, I found that the weight of the meter stick to be 150 grams. The actual weight was 149.3, so I was only 0.7 grams off.
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