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Holding period return

In finance, holding period return (HPR) is the total return on an asset or portfolio over the period during which it was held. It ... more

Beta distribution (variance)

In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] parametrized ... more

Mohr–Coulomb failure criterion

Mohr–Coulomb theory is a mathematical model describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as ... 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
Backlash (due to operating center modifications)

In mechanical engineering, backlash, sometimes called lash or play, is clearance or lost motion in a mechanism caused by gaps between the parts. It can be ... more

Backlash (due to tooth thickness changes)

In mechanical engineering, backlash, sometimes called lash or play, is clearance or lost motion in a mechanism caused by gaps between the parts. It can be ... more

Thin lens formula

A lens is a transmissive optical device which affects the focusing of a light beam through refraction. A simple lens consists of a single piece of ... more

Boltzmann distribution in mechanics

In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution, probability measure, or ... more

Discounting

Discounting is a financial mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a ... more

Reduced specific volume

In thermodynamicsIn thermodynamics, the reduced properties of a fluid are a set of state variables normalized by the fluid’s state properties at its ... more

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