Question

tammy and Theresa are at the park. if tammy weighs 120lbs and Theresa weighs 60lbs, where should the fulcrum be located on a 12 foot teeter totter

Answer 1

The fulcrum should be located 4 foot from either end of the teeter totter

Here, we want to know the position where the fulcrum should be placed.

The fulcrum should be placed in a position such that it supports both weight. The point at which the fulcrum is placed should be at a point where the weight of Tammy and Theresa is actually supported by the position of the fulcrum.

Let the fulcrum be placed at a point x, from either end of the teeter tooter.

Let us consider the diagrammatic representation below;

The representation shows how the arrangement should be.

If Tammy seats at a distance of x foot from the fulcrum, then Theresa will be at a distance (12-x) foot from the fulcrum

To balance the weight in the system, product of the weight and the distance from the fulcrum on one end of the fulcrum should be equal to the product of the weight and the distance from the fulcrum on one end of the fulcrum.

Thus, Mathematically;

`\begin{gathered} 120\text{ }*\text{ x = 60 (12 -x)} \\ \\ 120x\text{ = 720 - 60x} \\ \\ \text{Collect like terms;} \\ \\ 120x\text{ + 60x = 720} \\ 180x\text{ = 720} \\ \\ x\text{ = }(720)/(180) \\ \\ x\text{ = }4\text{ foot} \end{gathered}`

This means that the fulcrum should be located 4 foot from either end of the teeter totter