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Hyperboloid of two sheets equation

In mathematics, a hyperboloid is a quadric – a type of surface in three dimensions – . A hyperboloid of revolution of two sheets can be obtained by ... more

Distance between two points (three-space)

Distance is a numerical description of how far apart objects are. In analytic geometry, the distance between two points of the xyz-plane in three-space, ... more

Allowable Strength Design Load combination (eq5a)

In structural engineering, a structure is a body or combination of pieces of rigid bodies in space to form a fitness system for supporting loads. ... more

Allowable Strength Design Load combination (eq5b)

In structural engineering, a structure is a body or combination of pieces of rigid bodies in space to form a fitness system for supporting loads. ... more

Trip distribution zonal interchange model (related to trip origins and destinations)

Trip distribution (or destination choice or zonal interchange analysis) is the second component (after trip generation, but before mode choice and route ... 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
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

Sharpe ratio

In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance ... 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

Time to reach a required delta-v - rocket propulsion

Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with ... more

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