A steel beam that is 6.00 m long weighs 332 N. It rests on two supports, 3.00 m apart, with equal amounts of the beam extending from each end. Suki, who weighs 550 N, stands on the beam in the center and then walks toward one end. How close to the end can she come before the beam begins to tip?

To determine how close Suki can come to the end of the beam before it begins to tip, we need to find the point of balance.

Let's start by calculating the weight of the beam itself. Given that the beam weighs 332 N, which is the total weight of the beam when it is evenly distributed across the supports. Since the beam is symmetrical and the supports are equidistant from the center, we can assume that each support carries an equal weight of the beam.

Therefore, the weight supported by each of the two supports is 332 N / 2 = 166 N.

Now, let's consider the weight of Suki. Suki weighs 550 N, and she stands in the center of the beam. As she walks towards one end, her weight is no longer evenly distributed across the beam.

At the center of the beam, Suki's weight is evenly split between each support: 550 N / 2 = 275 N on each side of the fulcrum (center).

As Suki moves towards one end, the weight distribution changes. To calculate the weight on each side of the fulcrum, we need to consider the ratio of the distances from Suki to each support.

Let's call the distance from Suki to the left support (where she is walking towards) x. Since the total distance between the supports is 3.00 m, the distance from Suki to the right support is 3.00 m - x.

Now we can calculate the weight on each side of the fulcrum:

Weight on the left side of the fulcrum = (275 N * (3.00 m - x)) / 3.00 m
Weight on the right side of the fulcrum = (275 N * x) / 3.00 m

For the beam to remain in balance, the clockwise (right side) torque must be equal to the counterclockwise (left side) torque. Torque is calculated by multiplying the weight by the perpendicular distance from the fulcrum.

Since the distances from each support to the center of the beam are equal (1/2 of the total distance), the torque equation becomes:

Right side torque = (Weight on the right side) * (distance from fulcrum to the right support)
Left side torque = (Weight on the left side) * (distance from fulcrum to the left support)

Setting these two torques equal to each other, we have:

(275 N * x) / 3.00 m * (1.50 m) = (275 N * (3.00 m - x)) / 3.00 m * (1.50 m)

Simplifying the equation, we get:

x = 1.50 m

Therefore, Suki can come as close as 1.50 m to the end of the beam before it begins to tip.