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Absolute Magnitude of a Star - with parallax

Absolute magnitude is the measure of a celestial object’s intrinsic brightness. It is the hypothetical apparent magnitude of an object at a standard ... 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
Planet Formation Equation - "Clearing the neighbourhood"

“Clearing the neighbourhood around its orbit” is a criterion for a celestial body to be considered a planet in the Solar System. This was one ... more

Absolute Magnitude of a Star - with luminosity distance

Absolute magnitude is the measure of a celestial object’s intrinsic brightness. It is the hypothetical apparent magnitude of an object at a standard ... more

Specific Gas Constant - related to the Boltzmann constant

The ideal gas constant, denoted by the symbol R or R) is a physical constant which is featured in many fundamental equations in the physical sciences, ... more

Cauchy–Lorentz distribution (probability density function)

In probability and statistics,the Cauchy distribution, is a continuous probability distribution. The probability density function (pdf), or density of a ... more

Particle diameter (phi scale)

Particle size, also called grain size, refers to the diameter of individual grains of sediment, or the lithified particles in clastic rocks.
Size ... more

Specific gas constant

The ideal gas constant, denoted by the symbol R or R) is a physical constant which is featured in many fundamental equations in the physical sciences, ... more

Fourier Number (mass)

The Fourier number (Fo) or Fourier modulus, is a dimensionless number that characterizes heat conduction. It is the ratio of diffusive/conductive ... more

Reynolds number

In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that is used to help predict similar flow patterns in different fluid flow ... more

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