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Force between two nearby magnetized surfaces

The Gilbert model assumes that the magnetic forces between magnets are due to magnetic charges near the poles. This model produces good approximations that ... more

Fermi–Dirac distribution

Fermi–Dirac statistics describes a distribution of particles over energy states in systems consisting of many identical particles that obey the Pauli ... 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

Pressure to depth (empirical formula - sea water)

In sea water, there is an approximate numerical equivalence between the change in pressure in decibars and the change in depth from the surface in meters. ... more

Metcalfe’s Law

Metcalfe’s law states that the value of a telecommunications network is proportional to the square of the number of connected users of the system ... more

Optical depth

In physics, optical depth or optical thickness, is the natural logarithm of the ratio of incident to transmitted radiant power through a material, and ... more

Radius of meniscus (surface tension)

In a sufficiently narrow tube of circular cross-section of radius “a”, the interface between two fluids forms a meniscus that is a portion of the surface ... more

Discriminant of the Quadratic Equation

In algebra, the discriminant of a polynomial is a function of its coefficients, typically denoted by a capital 'D’ or the capital Greek letter Delta ... more

Potential energy (electrostatic forces between two bodies)

Potential function for electrostatic forces between two bodies is the work required to move a charge from a point to any point in the electrostatic force ... 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

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