Have you ever sat on a seesaw with your friend? If so, you might have wondered why one of you rises while the other remains on the ground. This intriguing phenomenon is caused by the turning effect of forces, also known as Principles of Moments.
What is Moments?
Definition: The turning effect produced by a force acting on an object about a pivot point. It is mathematically given as the product of the force and the perpendicular distance from the pivot to the line of action of the force.
- Formula : Moment = Force × Perpendicular Distance
- Units : The unit for the moment of force is the Newton-meter (Nm)
What is pivot?
A pivot, also known as a fulcrum, is a fixed point or support around which a lever or other object rotates or balances. In the case of a seesaw it would be the middle point, and for a trolley, it would be the point connected to the wheels.
Now, let us make use of this formula to understand how the seesaw works.
Person A weighs 40kg while Person B weighs 80kg. Their weight would then be 400N and 800N respectively. Assuming that both Person A and Person B sit the same distance away from the pivot of the seesaw, the moment about the pivot by Person B would be greater than that of Person A. This causes Person A to rise while Person B remains seated on the ground.
If both Person A and Person B are both 1m away from the pivot,
Anti-clockwise moment about the pivot by Person B = 800N x 1m = 800Nm
Clockwise moment about the pivot by Person A = 400N x 1m = 400Nm
Since 800 Nm > 400Nm, the Anti-clockwise moment is larger than the clockwise moment and thus causing Person A to rise while Person B remains on the ground
If you still don’t fully understand it, here’s another example – Have you tried pushing a door from Point A instead of the handle? You would notice that it is much more difficult to do so.
We can apply the concept of moments to explain why door handles are placed on the opposite side of the door hinges, which act as the pivot. By increasing the distance between the force at the door handle and the pivot, we can increase the moment and make it easier to open or close the door. (Perpendicular distance from the pivot is greater). This is why wrenches have long handles, to increase the moment and make it easier to tighten bolts.
What is the Principle of Moments?
For an object to be in equilibrium (i.e., not rotating), the total clockwise moment about any point must be equal to the total anti-clockwise moment about that same point. This principle is crucial for understanding the balance of forces in real-life applications like seesaws, levers, and bridges.
So, how can two people on a seesaw be at equilibrium? If both Person A and Person B result in the same moment! Let’s take a look at an example.
Anti-clockwise moment = 450N x 1m = 450Nm
Clockwise moment = 300N x 1.5m = 450Nm
Since ACM = CM, by the principle of moments, they are in equilibrium and hence would not move
There are two scenarios that can occur,
Scenario 1: Both Person A and B have the same weight and are sitting equal distances apart
Scenario 2: Person B who is lighter who will only exert a 500N force will sit at the end of the seesaw, while Person A who is heavier that exert 1000N of force will sit at the halfway mark of the seesaw.
In both scenarios 1 and 2, the anticlockwise moment brought about by person A would be equal to the clockwise moment brought about by person B, thus, The seesaw would be at equilibrium and would not move.
Using the same concept of Principle of Moments, we would be able to find missing values such as the weight of an object or the distance at which an object is placed from the pivot.
We can calculate the Anticlockwise moment using the formula: Moments = Force x Perpendicular Distance
Anticlockwise moment = 200N x 1m = 200Nm
Since the seesaw is in equilibrium, by the Principle of Moments, we know that the sum of Anticlockwise moment = the sum of Clockwise moment.
Clockwise moment = 50N x d = 200Nm
Therefore, d = 4m
Center of Gravity
The center of gravity is the point at which the entire weight of an object seems to act. For uniform objects, like a uniform rod or a flat, symmetrical sheet, the center of gravity lies at its geometrical center (i.e. the middle).
Stability
Objects are classified based on their stability:
- Stable Equilibrium: An object will return to its original position after a slight tilt. This is because its center of mass is below the pivot point.
- Unstable Equilibrium: A slight tilt will cause the object to topple. Here, the center of mass is above the pivot point.
- Neutral Equilibrium: Tilting doesn’t affect the object’s position. The center of mass remains at the same height.
