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Generalized volatility for time T

In finance, volatility is a measure for variation of price of a financial instrument over time. An implied volatility is derived from the market price of a ... more

Energy – Momentum relation

In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating any object’s rest (intrinsic) ... 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
Hick's Law

Hick’s law, or the Hick–Hyman law, named after British and American psychologists William Edmund Hick and Ray Hyman, describes the time it takes for ... more

Logarithm of a number

The logarithm of a number with a positive base different of 1

... more

Near depth of field

In optics, particularly as it relates to film and photography, depth of field (DOF) is the distance between the nearest and ... more

Far depth of field

In optics, particularly as it relates to film and photography, depth of field (DOF) is the distance between the nearest and ... 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

Number density (Relation to Molar concentration)

Number density is an intensive quantity used to describe the degree of concentration of countable objects. For any substance, the number density n can be ... more

Active return

In finance, active return refers to that segment of the returns in an investment portfolio that is due to active management decisions made by the portfolio ... more

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