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Barlow's formula - sphere

In the pipeline industry it is neccecary to verify that pipe used for gathering, transmission, and distribution lines can safely withstand operating ... 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
Rule of Mixtures

In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material made up of continuous and ... more

Block and tackle - effort required to raise a given weight

A block and tackle is a system of two or more pulleys with a rope or cable threaded between them, usually used to lift or pull heavy loads.The formula used ... more

Exponential decay

A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. If the decaying quantity, N(t), is the number of ... 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

Wet bulk density of soil (total bulk density)

Bulk density is a property of powders, granules, and other “divided” solids, especially used in reference to mineral components (soil, gravel), ... more

Volume Fraction of the Fibers (Rule of mixtures)

In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material made up of continuous and ... more

Vertical Wind Profile - Logarithmic Law

Wind speed extrapolation

In wind energy studies, two mathematical models or 'laws’ have generally been used to model the vertical profile of ... more

Sagnac effect (phase difference)

The Sagnac effect, also called Sagnac interference, named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is ... more

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