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Darwin / Radau equation

In astrophysics, the Darwin / Radau equation gives an approximate relation between the moment of inertia factor of a planetary body and its rotational ... more

Area of a Torus

In geometry, a torus (pl. tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the ... more

Interior Volume of a Torus

In geometry, a torus (pl. tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the ... more

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
Gravitational Potential (spherical symmetry)

Within a uniform spherical body of radius R and density ρ the gravitational force g inside the sphere varies linearly with distance r from the center, ... more

Auger electron spectroscopy - Electron impact cross-section (account for matrix effects)

Auger electron spectroscopy is a common analytical technique used specifically in the study of surfaces and, more generally, in the area of materials ... more

Uniform gravitational field without air resistance (altitude)

Free fall is any motion of a body where its weight is the only force acting upon it. If gravity is the only influence acting, then the acceleration is ... more

Bernoulli's principle

Bernoulli’s principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with an increase in dynamic ... more

Radau parameter - related to Darwin / Radau equation

In astrophysics, the Darwin / Radau equation gives an approximate relation between the moment of inertia factor of a planetary body and its rotational ... more

Uniform gravitational field without air resistance (velocity)

Free fall is any motion of a body where its weight is the only force acting upon it. Falling in air, as long as the force of gravity on the object is much ... more

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