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Angular Momentum

In physics, angular momentum, moment of momentum, or rotational momentum is a measure of the amount of rotation an object has, taking into account its ... more

Pearson's moment coefficient of kurtosis (excess kurtosis)

In probability theory and statistics, kurtosis is any measure of the “tailedness” of the probability distribution of a real-valued random ... more

Ripple factor

For the root mean square value of the ripple voltage, the calculation is more involved as the shape of the ripple waveform has a bearing on the result. ... 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
Time to reach specific temperature (related to Biot and Fourier numbers)

The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations. Gives a simple index of the ratio of the heat transfer resistances ... more

Flux (as a single scalar)

Flux is two separate simple and ubiquitous concepts throughout physics and applied mathematics. Within a discipline, the term is generally used ... more

Euler–Poincare characteristic( nonconvex polyhedra )

n mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler–Poincaré characteristic) is a ... more

Αxial stiffness for an element in tension

The stiffness of a body is a measure of the resistance offered by an elastic body to deformation.
Tension describes the pulling force exerted by each ... more

Number density

Number density is an intensive quantity used to describe the degree of concentration of countable objects. Volume number density is the number of specified ... more

Miles Equation

In 1954, Miles developed his version of this equation for GRMS as he was researching fatigue failure of aircraft structural ... more

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