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Parallel Plate Capacitor (considering the material)

The capacitance of a two parallel plates capacitor both of area A separated by a distance d is calculated by the area of overlap of the two plates, ... 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

Sherwood Number for a single sphere

The Sherwood number (Sh) is a dimensionless number used in mass-transfer operation. It can be further defined as a function of the Reynolds and Schmidt ... more

Radiant Exitance (real surface)

In radiometry, radiant exitance is the radiant flux emitted by a surface per unit area, and spectral exitance is the radiant exitance of a surface per unit ... more

Intendation area for Vickers hardness test

The basic principle of the Vickers hardness test, as with all common measures of hardness, is to observe the questioned material’s ability to resist ... 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
Degree of dissociation of a weak electrolyte

The degree of dissociation of a weak electrolyte is proportional to the inverse square root of the concentration, or the square root of the dilution

... more

Fatigue (Miner’s Rule)

In materials science fatigue occurs when a material is subjected to repeated loading and unloading. The failure of the material occurs when there are k ... more

Magnetic field of a solenoid

The magnetic field in the volume of a long, thin loop of wire, wrapped around a metallic core (solenoid) when an electric current is passed through it, ... more

Mach Number (subsonic compressible flow)

In fluid mechanics, Mach number (M or Ma) is a dimensionless quantity representing the ratio of speed of an object moving through a fluid and the local ... more

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