In an experiment to verify the laws of equilibrium, the centre of gravity and the weight of a metre stick were found - Leaving Cert Physics - Question 1 - 2016

The weight of the metre stick was measured using a Newton balance or weighing scales. The mass of the stick was obtained, and then this mass was multiplied by the acceleration due to gravity (g = 9.81 m/s²) to calculate the weight.

The upward forces acting on the metre stick were determined by using Newton balances to measure the forces applied upward, while the downward forces included the known weights attached to the stick, as well as its weight, which was previously calculated.

One possible reason the centre of gravity is not at the 50.0 cm mark is that the stick may have been worn on one side, or there could be a hole in one side, making it not uniform in its mass distribution.

The net force acting on the metre stick can be calculated by summing the upward forces and the downward forces.

Upward forces: $ext{Total Upward Force} = 3.9 ext{ N} + 4.1 ext{ N} = 8.0 ext{ N}$

Downward forces: $ext{Total Downward Force} = 2 ext{ N} + 3 ext{ N} + 2 ext{ N} + 1.1 ext{ N} = 8.1 ext{ N}$

Net vertical force can then be calculated as: $ext{Net Vertical Force} = ext{Upward Force} - ext{Downward Force} = 8.0 ext{ N} - 8.1 ext{ N} = -0.1 ext{ N}$

The moment about a point is calculated using the formula: $ext{Moment} = ext{Force} imes ext{Displacement}$

Clockwise moments at the 40 cm mark: $ext{Clockwise Moment} = (2 ext{ N} imes 0.52) + (1.1 ext{ N} imes 0.102) + (3.9 ext{ N} imes 0.004) = 1.3082 ext{ Nm}$

Anticlockwise moments: $ext{Anticlockwise Moment} = (2 ext{ N} imes 0.24) + (4.1 ext{ N} imes 0.20) = 1.3 ext{ Nm}$

Summing both moments: $ext{Sum of Moments} = 0.01 ext{ Nm}$

According to the laws of equilibrium, the net vertical force should equal zero, and the sum of the moments about any point should also equal zero. In this case, the net vertical force was calculated to be -0.1 N, which indicates an imbalance, suggesting that the system is not in equilibrium. Additionally, the sum of the moments about the point was found to be close to zero, which verifies the concept of balancing moments in equilibrium.