The seesaw principle: As you probably know, any two persons can balance each other
when sitting on opposite sides of a seesaw, regardless of their weights. It is only necessary
that each person contribute the same moment — calculated by multiplying the person’s
weight times the distance to the fulcrum. For example, if an 80-
pound child sits at one end of a 20-foot plank, 10 feet from the
fulcrum, a 200-pound adult can balance this system. Tell how.
200 x = 10 * 80
x = 4
To balance the system, we need to ensure that the moments (torques) exerted by both the child and the adult are equal. The moment is calculated by multiplying the weight of an object by its distance from the fulcrum.
In this case, we have an 80-pound child sitting 10 feet from the fulcrum on one side of the seesaw. To calculate the moment, we multiply the weight (80 pounds) by the distance from the fulcrum (10 feet), giving us a moment of 800 foot-pounds.
To balance the system, we need to find the distance from the fulcrum where the 200-pound adult should sit. Let's call this distance "x."
Using the principle of moments, we can set up an equation to find the value of "x." The equation states that the moment exerted by the child should be equal to the moment exerted by the adult.
So, we have:
80 pounds * 10 feet = 200 pounds * x feet
Simplifying the equation, we can divide both sides by 200 pounds:
8 feet = x
Therefore, the 200-pound adult should sit 8 feet from the fulcrum on the other side of the seesaw to balance the system.
It's important to note that in this example, both individuals are balanced despite having different weights because the moments they exert are equal.