explorers in the jungle find an ancient monument in the shape of a large isosceles triangle. the monument is made from tens of thousands of small stone blocks of density 3 800 kg/m^3. the monument is 15.7 m high and 64.8 m wide as its base and is everywhere 3.6m 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 block to put them in position while building the entire monument? note the gravitational potential energy of an object-earth systen is give 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

Question

explorers in the jungle find an ancient monument in the shape of a large isosceles triangle. the monument is made from tens of thousands of small stone blocks of density 3 800 kg/m^3. the monument is 15.7 m high and 64.8 m wide as its base and is everywhere 3.6m 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 block to put them in position while building the entire monument? note the gravitational potential energy of an object-earth systen is give 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

Answer 1

To calculate the work done by the laborers in positioning the stone blocks to build the monument, we need to find the gravitational potential energy of each individual block and then sum it up for all the blocks.

First, let's find the mass of one stone block. The volume of each block can be calculated by multiplying the height, width, and thickness:

Volume = height x width x thickness
Volume = 15.7 m x 64.8 m x 3.6 m

Since the blocks have a density of 3,800 kg/m^3, we can find the mass using the formula:

Mass = Density x Volume
Mass = 3,800 kg/m^3 x (15.7 m x 64.8 m x 3.6 m)

Now that we have the mass of one block, we can calculate the gravitational potential energy (Ug) using the given formula:

Ug = Mass x g x ycm

where g is the acceleration due to gravity and ycm is the elevation of the center of mass above the reference level.

Considering that the reference level is the ground level where the blocks originally lay, we can assume ycm as the height of the block since the monument is standing erect.

Now, let's calculate the work done for one block. We can use the formula:

Work = Ug

Given that g is approximately 9.8 m/s^2 (acceleration due to gravity on Earth), we can calculate the work done for one block:

Work = Mass x g x ycm

Multiply the mass of one block by g and the height of the block to find the work done for one block.

Finally, multiply the work done for one block by the total number of blocks (tens of thousands) to get the total work done by the laborers to build the entire monument.

Note: This calculation assumes that the blocks were lifted vertically, without any additional complications or changes in elevation.