We unconsciously balance objects every day, but rarely think about the conditions that must take place to achieve balance. In this activity, students define an object’s centre of gravity by balancing a ruler.
The word “balance” can mean many things. We can talk about a balanced breakfast, a balanced pocketbook, or a balanced lifestyle. In science, we say that an object is balanced if it is not moving. When an object is balanced, it is in a state of equilibrium. Any forces on the object are balanced by forces in the opposite direction.
The centre of gravity is the average position of the force of gravity on an object. Sometimes it is at the object’s geometric centre (e.g. ruler), whereas other times it isn’t (e.g. ruler with an eraser on one end). An object can be balanced if it’s supported directly under its centre of gravity.
To balance a ruler horizontally on a finger, the finger must be directly under the ruler’s centre of gravity. In this case, the ruler’s centre of gravity is the same as its mid-point since the ruler is symmetrical and has equal mass along its length. It is not possible to balance the ruler unless its centre of gravity is over your finger. You can find the centre of gravity of the ruler by sliding your fingers from the ends towards the middle. Observe carefully and you’ll notice that only one finger moves at a time. As you slide your fingers, the force of friction pushes back. The more weight on your finger, the greater the force of friction. One of your fingers is supporting slightly more of the ruler’s weight than the other; that finger gets “stuck.” The other finger will move until it is the one supporting the most weight, then it will get stuck instead. Friction makes sure that when your fingers meet they are both supporting the same amount of weight.
When you add an eraser to one end of the ruler, the balance point is no longer in the centre of the ruler, it is closer to the weighted end. The centre of gravity is the exact spot on the ruler where there is the same amount of weight on both sides. Once you change the weight anywhere on the ruler, the centre of gravity changes too.
When you balance the ruler or metre stick on its end, it’s easier to find the balance point, but harder to keep the stick balanced. The centre of gravity is quite high, and the stick tips over easily. You need to keep moving your finger to keep it under the centre of gravity.