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Gamma Function

In mathematics, the gamma function (represented by the capital Greek letter Γ) is an extension of the factorial function, with its argument shifted down by ... more

Gearing reduction ratio

Harmonic Drive is the brand name of strain wave gear trademarked by the Harmonic Drive company, and invented in 1957 by C.W. Musser.

It is very ... more

Gustafson's Law

In computer architecture, Gustafson’s law (or Gustafson–Barsis’s law) gives the theoretical speedup in latency of the execution of a task at ... more

Miller's Rule

In optics, Miller’s rule is an empirical rule which gives an estimate of the order of magnitude of the nonlinear coefficient.

More formally, ... 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
Saturated Adiabatic Lapse Rate

The lapse rate is defined as the rate at which atmospheric temperature decreases with increase in altitude. The terminology arises from the word lapse in ... more

Tractive Force - Steam locomotives

As used in mechanical engineering, the term tractive force can either refer to the total traction a vehicle exerts on a surface, or the amount of the total ... more

Calibrated airspeed (CAS)

Calibrated airspeed (CAS) is indicated airspeed corrected for instrument and position error.

When flying at sea level ... more

Cross Section (flux)

The cross section is an effective area that quantifies the intrinsic likelihood of a scattering event when an incident beam strikes a target object, made ... more

Logit function

The logit function is the inverse of the sigmoidal “logistic” function or logistic transform used in mathematics, especially in statistics. ... more

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