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The log driver

Spruce tree logs cut in a forest are floated toward a mill down the river. All logs are cylindrical and cut to equal lengths of 5 m, but have a range of diameters. They have a density of 450 kg/m3. A log driver, with a mass of 70 kg and an average density of 1050 kg/m3 is driving the floating logs by riding one at a time.

a) Determine the minimum diameter of a log on which the log driver can step without sinking. What would happen if the log diameter were slightly smaller?

b) If the log driver is riding on a log with a diameter equal to twice the value found in (a), determine the depth of immersion of this log.

Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada. Image from YouTube

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