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The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is the radius of a sphere such that, if all the ... more

Mean angular motion - function of gravitational parameter

In orbital mechanics, mean motion (represented by n) is the angular speed required for a body to complete one orbit, assuming constant speed in a circular ... more

Apsidal precession

In celestial mechanics, apsidal precession is the precession (gradual rotation) of the line connecting the apsides (line of apsides) of an astronomical ... 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
Arbitrary Cherenkov emission angle

Cherenkov radiation, also known as Vavilov–Cherenkov radiation,[a] is electromagnetic radiation emitted when a charged particle (such as an electron) ... more

Magnetic Reynolds number (relationship to eddy current braking)

The dimensionless magnetic Reynolds number, is also used in cases where there is no physical fluid involved.

The magnetic Reynolds number is the ... more

Nodal Precession

Nodal precession is the precession of an orbital plane around the rotation axis of an astronomical body such as Earth. This precession is due to the ... more

Material Removal Rate

Machining is any of various processes in which a piece of raw material is cut into a desired final shape and size by a controlled material-removal process. ... more

Speed of Sound (air, ideal gases) - relative to molar mass

The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of the speed of sound is the ... more

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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