Most archaeologists believe that the ancient Egyptians used very long ramps while building the pyramids. (It's also likely that ancient Egyptians used levers and ramps in combination.) The ramps had to be long because long ramps are shallow, and the stones the Egyptians assembled into the pyramids were too heavy to lift up steep ramps. The stones in the upper layers of Khufu's pyramid have a mass of about $2 \times 10^3 \;\mathrm{kg}$ $(2000 \;\mathrm{kg})$ each. The pyramids were primarily built by farmers, laboring in the seasons when there was no farm work to do. Let's estimate that a single worker can exert a force big enough to pick a $60 \;\mathrm{kg}$ stone straight up. (This means $60 \;\mathrm{kg}$ can play the role of "mass B" from our analysis of a ramp.) What is the steepest slope for the ramp the ancient Egyptians could have used if each block was to be pushed (and pulled with ropes) by a team of 8 workers? You can neglect friction for this problem. Although there was friction between the ramp and stone blocks during construction of the pyramids, ancient Egyptians put the stones on sleds, likely lubricated with water, to reduce the friction as much as possible.

This is an estimation problem, so your answer only needs to be approximately correct.

 Aug 28, 2022

The steepest slope is 1.857.

 Sep 5, 2022

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