Explorers in the jungle find an ancient monument in the shape of a large isoscel

Question

Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle as shown in the figure below. The monument is made from tens of thousands of small stone blocks of density 2 222 kg/m3. The monument is 15.2 m high and 63.4 m wide at its base and is everywhere 2.70 m thick from front to back. Before the monument was built many years ago, all the stone blocks lay on the ground. How much work did laborers do on the blocks to put them in position while building the entire monument? Note: The gravitational potential energy of an object-Earth system is given by Ug = MgyCM, where M is the total mass of the object and yCM is the elevation of its center of mass above the chosen reference level. J

Explanation / Answer

Work W done in erecting monument is: W = mgh where m = mass in kg, g = 9.81 m/s² and h = average lifting height. The centre of gravity is at the average height through which the (small) blocks must be raised to build the monument. The height of the centre of gravity = h = 14.9/2 = 7.45 m giving: W = 2239 x 65.8 x 3.7 x 14.9 x 9.81 x 7.45 = 593,600 x 10³ Nm or Joules

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