Static Equilibrium Could Win You One Million Dollars

CBS’s hit show Survivor first aired on May 31, 2000 and has continued, currently in its 33^rd season! The show features individuals who must survive harsh conditions, play a strong social game, and compete in challenges on their way to winning a grand prize of one million dollars. Some of these challenges have extremely high stakes, with the winner gaining an “immunity idol” that prevents them from being eliminated from the game.

As I watched a recent episode, I noticed that the immunity challenge relied almost entirely on the idea of static equilibrium in rotational motion. The challenge involved contestants balanced on a thin beam, while having to keep a small statue balanced using only a long bamboo pole (see the image below)

In order to keep the statue balanced, contestants would have to use their arm muscles to ensure that the bamboo pole maintained static equilibrium. The bamboo pole is ten feet long, or 3.05 meters. For this post, we will treat the bamboo pole as a uniform rod with a mass of one kilogram, as bamboo is an extremely light wood. Assuming the contestants back arm is the pivot point, and the front arm is applying a force of 30 degrees above horizontal, one meter from the back arm, we can calculate the force needed to maintain static equilibrium.

For static equilibrium,

 Using the free body diagram below, these three conditions will allow us to solve for both the magnitude of force exerted by the front arm, as well as the magnitude of force exerted by the back arm and the angle at which it acts.

To view the challenge this post is based on, visit: http://www.cbs.com/shows/survivor/video/642C2E55-51D6-0014-C840-8D39705ADE4F/survivor-reward-challenge-ferryman/