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Walking the plank



In a show I recently stumbled upon, a man was told to walk the plank. This plank was nailed down, but considering a plank that wasn't nailed down, one could find the length at which to extend the plank off the ship so that it wouldn't tip over when a person with a known mass walked across it. To calculate this, one has to think about the torques applied to the plank. The torques applied, assuming the person is at the end of the plank and the plank has a uniform mass, is only the torque applied by the person and the plank. The torque provded by the person is calculated by the person's mass multiplied by the acceleration due to gravity multiplied by the person's distance from the position at which the plank is being pivoted. The torque provided by the plank is the plank's mass multiplied by the acceleration due to gravity and the plank's distance from the pivot to its center of mass. An equation can then be solved by knowing that if the plank doesn't rotate, its net torque is zero, and therefore the torque provided by the person is equal to the torque provided by the plank. By setting up this equation the position at which the plank should be placed can be determined.


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