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Stress-Optic Law

Photoelasticity is an experimental method to determine the stress distribution in a material.Unlike the analytical methods of stress determination, ... more

Simple gear train with two gears (Torque ratio)

The gear ratio of a gear train, also known as its speed ratio, is the ratio of the angular velocity of the input gear to the angular velocity of the output ... 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
Abbe number ( V-number)

Abbe number , is a measure of the material’s dispersion in relation to the refractive index, with high values of V indicating low dispersion (low ... more

Albedo - correlation with Absolute Magnitude and Diameter

Albedo (/ælˈbiːdoʊ/), or reflection coefficient, derived from Latin albedo “whiteness” (or reflected sunlight) in turn from albus ... more

Shaft work

Energy transmission with a rotating shaft is very common in engineering practice. Often the torque T applied to the shaft is constant which means that the ... more

Acousto-optic deflector

An acousto-optic deflector spatially controls the optical beam. In the operation of an Acoustic-optic deflector the power driving the acoustic transducer ... more

Reynolds number

In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that is used to help predict similar flow patterns in different fluid flow ... more

Geometric series (sum of the numbers)

A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous ... more

Geometric progression (nth term)

A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous ... more

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