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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
Péclet number (for mass transfer)

The Péclet number (Pe) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum. It is named after the French ... more

Space Diagonal - Rectangular cuboid

In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. While mathematical ... more

Péclet number (for heat transfer)

The Péclet number (Pe) is a class of dimensionless numbers relevant in the study of transport phenomena in a continuum. It is named after the French ... more

Security characteristic line

Security characteristic line (SCL) is a regression line, plotting performance of a particular security or portfolio against that ... more

Worksheet 292

What is the cost of running a 0.600-kW computer 6.00 h per day for 30.0 d if the cost of electricity is $0.120 per kW ⋅ h ?

Multiplication

where t is the total consumption time, td is the days of consumption and th the hours of consumption per day

Power-average (related to Work)

where P is Power consumption rate, E is the energy supplied by the electricity company and t is consumption time

keywords:
ballistics

Multiplication

where C is the total cost and CkW is the cost per kilowatt hour

Reference : OpenStax College,College Physics. OpenStax College. 21 June 2012.
http://openstaxcollege.org/textbooks/college-physics
Creative Commons License : http://creativecommons.org/licenses/by/3.0/

Effective diffusivity in porous media

A porous medium (or a porous material) is a material containing pores (voids). The skeletal portion of the material is often called the ... more

Fermi–Dirac distribution

Fermi–Dirac statistics describes a distribution of particles over energy states in systems consisting of many identical particles that obey the Pauli ... more

Tractive Force - Steam locomotives

As used in mechanical engineering, the term tractive force can either refer to the total traction a vehicle exerts on a surface, or the amount of the total ... more

Roll-Off - First Order

Roll-off is the steepness of a transmission function with frequency, particularly in electrical network analysis, and most especially in connection with ... more

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