Meter Stick Challenge

In step one, we discussed the meter stick's center of gravity, and the torque on the meter stick depending on where it was located on the table and how much weight was added to the end.

In step two, we decided a plan on how to solve for the mass of the meter stick using the stick and a 100g lead weight. We were not allowed to use a scale. We found the tipping point of the stick without a weight on it (this is its center of gravity), which was 49.5 cm. We also found its tipping point with the weight which was 71 cm. We realized that the torque and center of gravity would be the same with or without the weight, which allowed us to solve for the mass, because torque = force times lever arm. When we found the weight of the meter stick, we could convert it to mass using w = mg. 

In step 3, which we performed as a class, my partner Princess and I  found that our meter stick had a different center of gravity than the others, causing our mass to be different. In the corrected method, we first had to know that the counter clockwise torque is equal to the clockwise torque. Since torque = force times lever arm, we could calculate the weight of the meter stick by plugging in the proper units in their respective places. The lever arm when it was balanced with the weight was .3 m, but we didn't know the force (this would be what we solved for, and it was the clockwise torque). The lever arm with the weight with a counter clockwise torque was .2 m with force of .98 (on the center of gravity). Thus we were able to solve for force and mass. The resulting number must be multiplied by 2, because it equals only half the mass of the meter stick.

The following link is a depiction of the meter stick on the table with the mass:
https://docs.google.com/drawings/d/1JH6rNL7vy14oYnYhB5W25tmBF3VMLc3q7PvhRTb97h0/pub?w=960&h=720

How to solve for the mass of the meter stick:

1) counter clockwise torque = clockwise torque
    Force time lever arm = force times lever arm

2) w = mg
    w = .1 (9.8)
    w = 0.98 N

3) F(.3) = (.98)(.2)
    F(.3) = .196
    F = .65 N

4) w = mg
   .65 = m(9.8)
   .066 kg = m