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Critical Buckling Compressive Loading of a Plate

In science, buckling is a mathematical instability that leads to a failure mode.

When a structure is subjected to compressive stress, buckling may ... more

Birch's Law

Birch’s law establishes a linear relation of the compressional wave velocity of rocks and minerals of a constant average atomic weight with density ... more

Graveyard Orbit - Minimum Perigee Altitude

A graveyard orbit, also called a junk orbit or disposal orbit, is a supersynchronous orbit that lies significantly above synchronous orbit, where ... more

Charles's law

Charles’ law is an experimental gas law which describes how gases tend to expand when heated. When the pressure on a sample of a dry gas is held ... 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
Mixing ratio (mole ratio)

In chemistry and physics, the dimensionless mixing ratio is defined as the abundance of one component of a mixture relative to that of all other ... more

Poisson Distribution

In probability theory and statistics, the Poisson distribution (French pronunciation [pwasɔ̃]; in English usually /ˈpwɑːsɒn/), named after French ... more

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

Present value of a perpetuity (Present Value of Int Factor Annuity)

A perpetuity is payments of a set amount of money that occur on a routine basis and continues forever. Present value of a perpetuity is an infinite and ... more

Power average (related to Work)

Power is the rate of doing work. It is equivalent to an amount of energy consumed per unit time. The same amount of work is done when carrying a load up a ... more

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