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Petroff's Law - Torque required to shear the lubricant film (for small radial loads)

In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more

Lateral earth active pressure (Rankine theory)

Lateral earth pressure is the pressure that soil exerts in the horizontal direction. Rankine’s theory, is a stress field solution that predicts ... more

Critical Speed of a Rotating Shaft - Rayleigh–Ritz method

In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating ... more

Quadrilateral's length of the diagonals

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. The interior angles of a simple (and planar) quadrilateral add up to ... more

Orthodiagonal quadrilateral (medians of the four triangles)

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. An orthodiagonal quadrilateral is a quadrilateral in which the ... more

Orthodiagonal quadrilateral (altitudes of the four triangles)

A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. An orthodiagonal quadrilateral is a quadrilateral in which the ... more

Seiche - Longest natural period (Merian's formula)

A seiche (/ˈseɪʃ/ SAYSH) is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related ... more

Petroff's Law - Bearing coefficient of friction

In the design of fluid bearings, the Sommerfeld number (S), or bearing characteristic number, is a dimensionless quantity used extensively in hydrodynamic ... more

Freezing point depression (cryoscopy)

Colligative properties are properties of solutions that depend upon the ratio of the number of solute particles to the number of solvent molecules in a ... 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

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