Title: Exciting Seesaw Experiment with Guests!

Question:

After dinner two guests decide to use a 3.0 m long 5.0 kg board as a seesaw, using a small bench as a fulcrum. An 82 kg man sits on one end and a 64 kg woman sits on the other end. Where should the bench be located (the distance from the 82 kg man) so that the board balances?

Answer:

The bench should be located 1.8 meters from the 82 kg man for the board to balance.

Explanation:

We have a thrilling setup for an experiment here! Imagine using a board as a seesaw with guests sitting on either end. In this case, an 82 kg man and a 64 kg woman are the guests participating in the experiment.

To achieve balance on the seesaw, we need to determine where the small bench fulcrum should be placed. The torques on each side of the seesaw must be equal for it to balance properly.

Let's use the torque equation: Torque = Force * Distance. The 82 kg man sits on one end at a distance of x meters from the fulcrum, and the 64 kg woman sits on the other end at a distance of (3.0 - x) meters.

By setting up and solving the torque equation, we find that the bench should be located 1.8 meters from the 82 kg man for the seesaw to balance perfectly. A placement of 5.4 meters, as previously tried, would result in an imbalance and make the seesaw unsteady.