Finding the Mass of a Meter Stick Without Using a Scale Lab

STEP 1:

This picture depicts an unbalanced meter-stick with a torque. It is unbalanced because the center of gravity is not supported. The force comes out of the center of gravity, causing it to tilt counter-clockwise. The lever arm is the distance from the Center of Gravity to the base of support. A Torque=(Force)(Lever Arm)

Step 2: 

This picture depicts a balanced meter-stick. It is balanced because the Center of Gravity is supported. The force comes out of the Center of Gravity, and since it is within the support, the meter-stick will not tilt or topple over. There is no lever arm because the meter-stick is balancing on its Center of Gravity.

Step 3:

A 100g weight was added to the meter-stick, which changed the system's center of gravity, but not the Center of Gravity of the meter-stick itself. On lever arm is from the edge to the base of support, and the other is from the base of support to the meter-stick's center of gravity. Since the Lever arm from the weight to the base of support is longer than the other one, to make the two Torques equal, which has to happen for something to be balanced, there needs to be a greater force on the side with the shorter lever arm. That makes the equation (Force(a))X(Lever Arm(a))=(Force(b))X(Lever Arm(b)) true.

Part 3:

Torque=Force X Lever Arm

We found the Center of Gravity of the meter-stick by itself, which was 50.25 cm. When we added the 100g weight, the lever arm with the weight is 29.5 cm, and the other lever arm is 20.75 cm. w=mg, which means w=0.1Kg*9.8-- Weight=0.98N Since I know the lever arm and the force of one side of the meter-stick, I can find the Torque. Torque=(0.1X9.8)(29.5)--- Torque=28.9 N cm. This is the Torque for both sides because for something to be ballanced, the clockwise Torque= the counter-clockwise Torque. This means that 28.91=20.75(F)--- 1.39=Force. w=mg---- 1.39=m(9.8)---1.39/9.8=0.1418 which, when converted from Kg to g, you get 141.8g. When we weighed our meter-stick, the weight was 142.9g.