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Sersic profile

The Sérsic profile (or Sérsic model or Sérsic’s law) is a mathematical function that describes how the intensity I of a galaxy varies with distance ... more

Temprature of a planet

Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by ... more

Sersic profile (in terms of the half-light radius, Re)

The Sérsic profile (or Sérsic model or Sérsic’s law) is a mathematical function that describes how the intensity I of a galaxy varies with distance ... more

Mach Number (supersonic, calculated from Pitot Tube Pressure)

In fluid mechanics, Mach number (M or Ma) is a dimensionless quantity representing the ratio of speed of an object moving through a fluid and the local ... more

Slant Range

In radio electronics, especially radar terminology, slant range is the line-of-sight distance between two points which are not at the same level relative ... more

Rectangle area

Rectangle is any quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its ... more

Volume of a Parallelepiped (Cramer's Rule)

Parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). Any of the three ... more

Angle of elevation (for object following a ballistic trajectory)

A trajectory or flight path is the path that a moving object follows through space as a function of time. A trajectory can be described mathematically ... more

Hawking Radiation - Temperature of a black body (or a black hole)

A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A black hole ... 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

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