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Orbital Period - as a function of central body's density

The orbital period is the time taken for a given object to make one complete orbit around another object.

When mentioned without further ... more

Gravitational Potential

In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that is done by the force of ... more

Mean orbital speed for negligible mass' bodies

The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around ... more

Vis-Viva Equation

In astrodynamics, the vis viva equation, also referred to as orbital energy conservation equation, is one of the fundamental equations that govern the ... more

Frequency (Doppler effect for a moving black body)

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

Nq bearing capacity factor

Karl von Terzaghi was the first to present a comprehensive theory for the evaluation of the ultimate bearing capacity of rough shallow foundations. This ... more

Compton wavelength

The Compton wavelength is a quantum mechanical property of a particle. The Compton wavelength of a particle is equivalent to the wavelength of a photon ... more

Leaning ( for bikes and motorcycles)

Bikes must lean during a turn to balance the relevant forces: gravitational, inertial, frictional, and ground support. The angle of lean can be ... more

Worksheet 341

The aweÔÇÉinspiring 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
Temprature of a black body

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

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