Balanced Torques and Center of Gravity

Balanced Torques and Center of Gravity

Objective:  

     To investigate the conditions for rotational equilibrium of a rigid bar and to determine the center of gravity of a system of masses.

Materials: 

• 1 Meter Stick
• 3 Meter Stick clamps (knife edge clamp)
• 1 Balance Support
• 1 Mass Set of Various Masses 
• 3 Weight hangers
• 1 Unknown Masse
• 1 Balance                                             

Procedure:

1. Balance the meter stick in the knife edge clamp and record the position of the balance point.

2. Select two different masses (100 grams or more each) and using the meter stick clamps and weight hangers, suspend one on each side of the meter stick support at different distances from the support. Adjust the positions so the system is balanced. Record the masses and positions. Sum the torques about your pivot point O and compare with the expected value.

3. Place the same two masses used above at different locations on the same side of the support and balance the system with a third mass on the opposite side. Record all three masses and positions. Calculate the net torque on this system about the point support and compare with the expected value.

4. Replace one of the above masses with an unknown mass. Readjust the positions of the masses until equilibrium is achieved, recording all values. Using the equilibrium condition for rotational motion, calculate the unknown mass. Measure the mass of the unknown on a balance and compare the two masses by finding the percent difference.

5. Place about 200 grams at 90 cm on the meter stick and balance the system by changing the balance point of the meter stick. From this information, calculate the mass of the meter stick. Compare this with the meter stick mass obtained from the balance.

6. With the 200 grams still at the 90 cm mark, imagine that you now position an additional 100 grams mass at the 30 cm mark on the meter stick. Calculate the position of the center of gravity of this combination (two masses and meter stick). Check your result by actually placing the 100 g at the 30 cm mark and balancing this system. Compare the calculated and experimental results.