A student investigated the laws of equilibrium for a set of co-planar forces acting on a metre stick - Leaving Cert Physics - Question 1 - 2014

The diagram should accurately reflect the forces acting on the metre stick, indicating 9 N and 12.5 N upward and 5 N and 15 N downward at their respective positions.

The total upward force can be calculated by adding the upward forces: $9 ext{ N} + 12.5 ext{ N} = 21.5 ext{ N}$.

The total downward force is the sum of the downward forces: $5 ext{ N} + 15 ext{ N} = 20 ext{ N}$.

According to the laws of equilibrium, the total upward force must equal the total downward force for an object to be in balance. Here, the upward force is 21.5 N and the downward force is 20 N. Since these values do not match, the system is not in equilibrium.

To calculate the anticlockwise moments, we take the moments produced by each upward force around the 0 mark:

• Moment due to 9 N at 10 cm: $9 ext{ N} imes 10 ext{ cm} = 90 ext{ N cm}$

• Moment due to 12.5 N at 62.5 cm: $12.5 ext{ N} imes 62.5 ext{ cm} = 781.25 ext{ N cm}$

• Total anticlockwise moment: $90 + 781.25 = 871.25 ext{ N cm}$.

Calculating the clockwise moments:

• Moment due to 5 N at 40 cm: $5 ext{ N} imes 40 ext{ cm} = 200 ext{ N cm}$

• Moment due to 15 N at 70 cm: $15 ext{ N} imes 70 ext{ cm} = 1050 ext{ N cm}$

• Total clockwise moment: $200 + 1050 = 1250 ext{ N cm}$.

For the system to be in equilibrium, the sum of anticlockwise moments must equal the sum of clockwise moments. Here, the anticlockwise moments total 871.25 N cm, while the clockwise moments total 1250 N cm. Since these values are not equal, the system is not in equilibrium, which illustrates the principle that these moments must balance.