Levon, who weights 153 lb, sits 6 ft from the seesaw support. Find the constant of variation.

To find the constant of variation for Levon sitting on a seesaw, we need to use the concept of a lever and the principle of moments in physics. When a person sits on a seesaw, they create a moment (or torque) around the pivot point (support) of the seesaw. The moment is the product of the force applied, which in this case is Levon's weight, and the distance from the pivot point where the force is applied, which is where Levon is sitting.

The moment (M) is calculated with the formula: M = force (F) × distance (d)

Levon's weight is the force, which needs to be converted to a force unit. Since force is typically measured in newtons (N) in the metric system, and weight is a force due to gravity, we must convert Levon’s weight from pounds to newtons. However, the constant of variation when dealing with the moment of a seesaw typically uses the weight as is and the distance, so we do not need to convert units in this particular case.

The distance is already given as 6 feet. Now we will find the moment created by Levon on the seesaw.

Given: - Levon's weight (F) = 153 lb - Distance from the support (d) = 6 ft

Moment is calculated as: M = F × d M = 153 lb × 6 ft

Now, the constant of variation (k) will be the ratio of the moment to the weight of Levon (this would also be equal to the distance if we had set the moment equal to the product of the weight and a constant, k, where M = k × weight). Since we are not solving for a person on the other side of the seesaw, and we simply need the constant of variation for Levon's position, k will be equal to the distance from the pivot point.

k = d k = 6 ft

So, the constant of variation is 6 feet. This means that for every pound of weight that Levon has, there are 6 foot-pounds of torque exerted on the seesaw about the support point.