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 3 854 kg/m3. The monument is 16.4 m high and 69.7 m wide at its base and is everywhere 3.50 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

Volume of ancient monument

= 0.5 * 16.4 * 69.7 * 3.50 = 2000.39 m3

Total mass of ancient monument

= 3854 * 2000.39 = 7709503.06 kg

The center of mass of a triangle is located at 1/3 of its perpendicular height

Ycm = 1/3 * height = 1/3 * 16.4 = 5.4667 m

Total work M * g * Ycm = 7709503.06 * 9.8 * 5.4667

= 413023777.268 J

= 4.13 * 108 Joules = 413 * 106 Joules

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