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Townsend avalanche (Townsend discharge)

The Townsend discharge is a gas ionization process where free electrons, accelerated by a sufficiently strong electric field, give rise to electrical ... more

Malus' law (polarized light)

A polarizer or polariser is an optical filter that passes light of a specific polarization and blocks waves of other polarizations.
When a perfect ... more

Numerical Aperture

In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can ... 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
Möbius strip (y- coordinate )

The Möbius strip or Möbius band, is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being ... more

Möbius strip (z- coordinate )

The Möbius strip or Möbius band, is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being ... more

Gaussian beam (Beam width or spot size)

In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are well ... more

Möbius strip (x- coordinate )

The Möbius strip or Möbius band, is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being ... more

Apsis - Periapsis maximum speed

An apsis, plural apsidesis a point of greatest or least distance of a body in an elliptic orbit about a larger body. For a body orbiting the Sun the ... more

Apsis - Apoapsis minimum speed

An apsis, plural apsidesis a point of greatest or least distance of a body in an elliptic orbit about a larger body. For a body orbiting the Sun the ... more

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