A seesaw is 4 meters long and is pivoted in the middle. There is a 350 N child on the left end. Where will a 540 N person have to sit to balance the seesaw?

Assume a distance of d from the fulcrum. Take moments about the fulcrum:

350*2-540d=0
d=1.296 m

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To determine where the 540 N person needs to sit in order to balance the seesaw, we can use the principle of moments.

The principle of moments states that for an object to be in rotational equilibrium, the sum of the moments acting on one side of the pivot must equal the sum of the moments acting on the other side of the pivot.

In this case, the pivot is in the middle of the seesaw, so we can consider the moments acting on the left and right sides separately.

On the left side:
- The child has a weight of 350 N.
- The distance from the child to the pivot is half the length of the seesaw, which is 4 meters / 2 = 2 meters.
- The moment can be calculated by multiplying the weight by the distance: Moment = 350 N * 2 m = 700 N·m.

On the right side:
- The person has a weight of 540 N.
- Let's denote the distance from the person to the pivot as x meters.
- The moment can be calculated by multiplying the weight by the distance: Moment = 540 N * x m = 540x N·m.

According to the principle of moments, the sum of the moments on both sides should be equal for the seesaw to balance:

700 N·m = 540x N·m.

To find the value of x, we can rearrange the equation:

x = 700 N·m / 540 N = 1.296 m.

Therefore, the 540 N person needs to sit at a distance of approximately 1.296 meters from the pivot in order to balance the seesaw.