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Surface wave magnitude scale

The surface wave magnitude (M_s) scale is one of the magnitude scales used in seismology to describe the size of an earthquake. It is based on measurements ... more

Pressure in a Contact Area between two spheres

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Corner sight distance

Corner sight distance (CSD) is the road alignment specification which provides a substantially clear line of sight so that the ... more

Pressure distribution on a Contact Area between a rigid cylinder and an elastic half-space

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. Hertzian contact stress refers to the localized ... more

Time Constant in digital electronic circuits

In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of ... more

Wave shoaling height

In fluid dynamics, wave shoaling is the effect by which surface waves entering shallower water change in wave height. It is caused by the fact that the ... more

Vertical Pressure variation of the Atmosphere of Earth( exponential function of height)

Vertical pressure variation is the variation in pressure as a function of elevation. The vertical variation is especially significant, as it results from ... more

Dirichlet kernel (In mathematical analysis)

The Dirichlet kernel is a collection of functions and its importance comes from its relation to Fourier series, that decomposes any periodic function or ... more

Worksheet 341

The aweÔÇÉinspiring 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
Richter magnitude scale

assigns a magnitude number to quantify the energy released by an earthquake. The Richter scale is a base-10 logarithmic scale, which defines magnitude as ... more

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