"Professor Povey's Perplexing Problems", written by Thomas Povey, is a great book with many intriguing and challenging maths and physics problems. Here, I upload my solution to some of the problems in the book.
This problem is from chapter 3: statics. Statics deals with the necessary conditions for a system to be in equilibrium, which in most cases directly corresponds to a condition whereby the net force and the net torque (or moment) about the center of mass of an object is equal to zero; i.e. no net force and no torque acts upon an object's center of mass. This particular problem deals with the force that would have been required by ancient Egyptians in using a rope to raise an obelisk.
A typical obelisk is said to have the following dimensions: height 37m, width 2.5m, and mass 450T (=4.5*10^5 kg). Assuming that g=9.81 ms^-2, The force required to raise the obelisk when it is tilted 15 degrees to the vertical axis would be:
F = (4.5*10^5) * (9.81/2) * ( ( (37/2.5) * tan(15deg) - 1) / ( (37/2.5) + tan(15deg) ) )
= 4.34*10^5 N, or 434 kN
Assuming that each person can generate a horizontal pulling force equivalent to about a third of their weight, the average force that a person generates by pulling on the rope would be (1/3) * mg = (1/3) * (75*9.81) = 245 N
Dividing 434 kN by 245N, the number of people needed to pull the obelisk can be found, which is: 434,000 / 245 = 1771. Thus, about 1700 ~ 1800 people are needed to pull the obelisk at 15 degrees to the vertical axis.
This would have certainly been the most intense game of tug of war in history.
Bibliography (Only the question is from the book; the solution is done by myself and checked if it matches Povey's solution in the book)
Povey, T. (2015). Professor Povey's perplexing problems: Pre-university physics and maths puzzles with solutions. London: Oneworld Publications.
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