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 2 851 kg/m3. The monument is 14.6 m high and 62.2 m wide at its base and is everywhere 3.90 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 the monument = 3.9 * 0.5 *14.6*62.2 =1770.834 m3 Centre of mass of the monument is at the centeroid of the isosceles triangle ,therfore height is h/3 which is the centre of massof isosceles triangle = 14.6/3=4.86 m

U=1770.834 *2851 * 9.81* 4.86= 2.4*10^8 J

work done by labourers = 2.4*10^8 J

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