The purpose of the setup is to show that the dowel can be balanced by adjusting the string to the dowel's center of mass, which suggests that Sydney has made a simple type of balance scale.
The image you've uploaded appears to be of a simple balance scale made using a dowel with deflated balloons attached to each end, suspended by a string. This setup is often used as a simple demonstration of a physical principle, likely meant to illustrate the concept of balance or equilibrium in a physics or science lesson.
To ensure the dowel remains horizontal and is in equilibrium, the center of mass must be directly below the point where the string is attached. If the balloons are of equal weight and the dowel is uniform, the system will balance.
There are no numerical calculations to show here because the concept is demonstrated visually and qualitatively. The purpose of the setup is to show that the dowel can be balanced by adjusting the string to the dowel's center of mass, which suggests that Sydney has made a simple type of balance scale.