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Effective interest rate

The effective interest rate, effective annual interest rate, annual equivalent rate (AER) or simply effective rate is the ... more

Freefall in Uniform Gravitational Field with Air Resistance (altitude)

In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In a Freefall in Uniform Gravitational Field with ... more

Lateral earth active pressure (Rankine theory)

Lateral earth pressure is the pressure that soil exerts in the horizontal direction. Rankine’s theory, is a stress field solution that predicts ... more

Acceleration of reciprocating piston with respect to crank angle

A piston is the moving component that is contained by a cylinder and is made gas-tight by piston rings. In an engine, its purpose is to transfer force from ... more

Optimum HDTV viewing distance

Optimum HDTV viewing distance is the distance that provides the viewer with the optimum immersive visual ... more

Lateral earth active pressure (Rankine theory for horizontal backfill)

Lateral earth pressure is the pressure that soil exerts in the horizontal direction. Rankine’s theory, is a stress field solution that predicts active and ... more

Front focal length (FFL)

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

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
Periodic compounding

Compound interest is interest added to the principal of a deposit or loan so that the added interest also earns interest from then on. This addition of ... more

Euler's theorem (excircles)

The circumscribed circle or circumcircle of a triangle is a circle which passes through all the vertices of the triangle. The center of this circle is ... more

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