Balanced Torques and Center of Gravity

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

Clamp 1: .02305 kg
Clamp 2: .0212 kg
Clamp 3: .0195 kg
Clamp 4: .0215 kg
m actual = .1469 kg
Meter stick: .091 kg
Balance point: .486 m

The meter stick balanced

2) C2 + .1 kg at .1 m                  C3 + .15 kg at .762 m

Meter stick with the two masses balanced

g*length*(C2+mass) = g*length*(C3+mass)

(9.8)(.386)(.0212+.1) + (9.8)(.276)(.0195+.15)

.45848N = .45846N

% difference = .0002%

- It is important to add the mass of the clamp into the calculations because they are not small enough to be negligible.

3) C3 + .15 kg at .19 m              C2 + .1 kg at .38 m                   C4 + .2 kg at .769 m

Meter stick balanced with three masses

g*length*(C3+mass) + g*length*(C2+mass) = g*length*(C2+mass)

(9.8)(.296)(.0195+.15) + (9.8)(.106)(.0212+.1) = (9.8)(.283)(.0215+.2)

.4917N + .1259N = .6143N

.6176N = .6143N

% difference = .0033%

4) C3 + .15 kg at .19 m              C2 + .1 kg at .38 m                 C4 + m at .86 m

Meter stick balanced looking for mass of meter stick

g*length*(C3+mass) + g*length*(C2+mass) = g*length*(C4+m)

(9.8)(.296)(.0195+.15) + (9.8)(.106)(.0212+.1) = (9.8)(.374)(.215+m)

.4917 +.1259 = (9.8)(.374)(.0215+m)

.6176 = (3.6652)(.0215+m)

.1685 = .0215+m

.147 = m

% difference = .07%

5) BP at .486 m                          New fulcrum at .78 m       C2 + 200 at .9 m

New fulcrum work and picture

- The clamp holding the meter stick shouldn't be included in the mass because it is holding it balanced not cause more or less mass on it to cause it to change the balance point.

Work and picture for masses at set points

Conclusion: This lab we worked with torque. We were able to find an equilibrium for different scenarios with a meter stick. I learned that there are several ways to add the clamps into the amount of mass on the clamp. Also, I learned that torque is force*lever arm. For us it was simple because there wasn't an angle to deal with. Some of the source of error would be the balance support. The piece supporting the stick wasn't exactly level by itself. Another is that there was a hole drilled into the stick. This changes where the balance point should be. Also, the table and the block of wood that the system was on could not have been balanced. To improve this lab, we would need a better meter stick and to make sure everything was level and working correctly.