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Worksheet 341

The awe‐inspiring Great Pyramid of Cheops was built more than 4500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres, and it was 146 m high (H), with a mass of about 7×10^9 kg. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging). Historians estimate that 20,000 workers spent 20 years to construct it, working 12-hour days, 330 days per year.

a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.

Division
Potential energy

b) Only a fraction of the workers lifted blocks; most were involved in support services such as building ramps, bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1000 of them and they consumed food energy at the rate of 300 Kcal/hour.

first we calculate the number of hours worked per year.

Multiplication

then we calculate the number of hours worked in the 20 years.

Multiplication

Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.

Multiplication
Multiplication

The efficiency is the resulting potential energy divided by the consumed energy.

Division
Specific Gas Constant - related to the Boltzmann constant

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Tuning fork (cylindrical prongs)

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Fermi–Dirac distribution

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Resistances connected parallel

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Standard change of reaction in Gibbs free energy

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Potential energy (electrostatic forces between two bodies)

Potential function for electrostatic forces between two bodies is the work required to move a charge from a point to any point in the electrostatic force ... more

Townsend avalanche (Townsend discharge)

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Capacitors in parallel connection

If two or more components are connected in parallel they have the same potential difference (voltage) across their ends. The potential differences across ... more

Ohm's Law

Ohm’s law states that the current through a conductor between two points is directly proportional to the potential difference across the two points, ... more

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