A student investigated the laws of equilibrium for a set of co-planar forces acting on a metre stick - Leaving Cert Physics - Question 1 - 2007

In the diagram, the forces should be illustrated as follows:

• Upward forces: 10 N at the right end and 15 N positioned at 80 cm.
• Downward force: 1.2 N at the centre of gravity, directly at the 50 cm mark. The forces should be clearly labeled.

The total upward force acting on the metre stick can be calculated by adding the upward forces: $ext{Total Upward Force} = 10 ext{ N} + 15 ext{ N} = 25 ext{ N}$

The total downward force acting on the metre stick is simply the weight of the metre stick, which is: $ext{Total Downward Force} = 1.2 ext{ N}$. Thus, if there are no other downward forces mentioned in the question, this remains the total.

In equilibrium, the sum of upward forces must equal the sum of downward forces. Since: $ext{Total Upward Force} = 25 ext{ N}$ and$ext{Total Downward Force} = 1.2 ext{ N}$, there seems to be an error since these values should be equal for equilibrium. Thus, it denotes that either the diagram has additional forces not accounted for, or there is a mistake in counting the forces.

The sum of the anticlockwise moments can be calculated by:

• Moment due to 15 N at 80 cm: $ext{Moment} = 15 ext{ N} imes (80 ext{ cm} - 0 ext{ cm}) = 15 ext{ N} imes 80 ext{ cm} = 1200 ext{ N cm}$
• Moment due to 10 N at 100 cm:
  $ext{Moment} = 10 ext{ N} imes (100 ext{ cm} - 0 ext{ cm}) = 10 ext{ N} imes 100 ext{ cm} = 1000 ext{ N cm}$

Thus, $ext{Total Anticlockwise Moment} = 1200 ext{ N cm} + 1000 ext{ N cm} = 2200 ext{ N cm}$

The downward forces create clockwise moments. The only downward force in this scenario is the 1.2 N acting at the 50 cm mark: $ext{Clockwise Moment} = 1.2 ext{ N} imes (50 ext{ cm} - 0 ext{ cm}) = 1.2 ext{ N} imes 50 ext{ cm} = 60 ext{ N cm}$

In equilibrium, the total anticlockwise moments must equal the total clockwise moments. We have:

• Anticlockwise Moment: 2200 N cm
• Clockwise Moment: 60 N cm

These values do not equal, indicating that the system is not in true equilibrium. The principle states that: $ext{Total Anticlockwise Moment} = ext{Total Clockwise Moment}$ When these values are not equal, it highlights an error in force applications or placements.