Problem 246: Ships ahoy
Hold on to your sails...The answer to this physics problem might sweep you away.
In writer Jules Verne’s famous adventure novel titled Mathias Sandorf, Captain Matifou uses his supernatural strength to perform heroic deeds. One such deed included stopping a newly built ship from colliding with a yacht by grabbing the rope that was tied to the nose of the ship. According to the story, Matifou wrapped the rope around a nearby pole three times and held it, stopping the ship and allowing the yacht enough time to pass by unharmed.
In the novel, Matifou’s act is described as requiring superhuman strength. But just how much force did this 19th century superhero need to hold the ship’s rope tight after wrapping it around the pole?
According to the book, the ship weighed 50 tons. The angle of the slide is 1/10, and the coefficient of friction between the rope and steel pole is around 1/3. Use Euler’s formula to calculate friction force as a function of the windings around a round pole — F=feka — and ultimately the amount of force Matifou needed to use to succeed at this heroic feat.