Mass of a Meterstick

During physics class we were instructed to determine the mass of a meter stick by using a meter stick and a weight. In order to fully comprehend the objective of this project it is important to identify where the center of gravity is located. In order to find this point balance the meter-stick without the weight first. For many meter sticks the center of gravity is located close to 50cm. Once you have determined the exact point where the meter-stick can balance you then place the weight on one end of the meter-stick and make it balance balance. For me this point was located at 30cm. We now have to identify that when 100 grams is added to the end of the meter stick, it will balance at 30cm. Torque is the tendency of an object to rotate around the axis of rotation. This can be calculated by multiplying the lever arm and the force on the object. Torque = lever arm x force When the object balances the torque on each side of the object is the same. We now know hat the lever arm of the meter-stick is 30cm but we need to determine the force acting on the meter stick. The 100 gram mass is our force since gravity is acting on the mass. We can convert this mass to weight (a force) by multiplying the mass by gravity (9.8 N/kg). Since gravity is in kg we first must convert the grams into kg which is .98 kg. Now that we have determined our lever arm is 30cm and our force is .98 N/kg we can determine the toque on one side of the meter-stick thus allowing us to find the total mass of the meter-stick. Once my group made this calculation we discovered that the torque on the system is 29.4. Once we found the torque, we determined that since the lever arm was 30 cm we had to subtract this amount by the entire lever arm when no weight is added to the system. Since the system in in equilibrium at 50cm, we subtracted the 30cm by 50cm. 20cm is our new lever arms and is vital when deriving the mass of the meter stick. Since we know the total torque we can reorganize the equation in order to find the mass. This equation would be; Torque/Lever arm= Force Once we calculated that the force equated to 1.47 we needed to convert this number to grams. We were able to do this by dividing this value by 9.8 (the force of gravity) and then multiplying by 100. This equated to the value of 150g. Once we weighted the meter stick, my group discovered that the actual weight of the meter stick was 150.4 grams. Since our estimation was off by only 0.4 grams my group was amazed and in shock. The picture below will show you how to set up the experiment. I have indicated that 30cm is where our meter stick balanced however this is different for every meter stick.