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Bending moments at any point along the span of a cantilevered beam with the free end supported on a roller

A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... more

Relation between Polarization density and Electric field in various materials

In classical electromagnetism, polarization density is the vector field that expresses the density of permanent or induced electric dipole moments 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
Hydraulic pump power

A hydraulic pump is a mechanical sourse of power that converts mechanical power into hydraulic energy (hydrostatic energy i.e. flow, pressure). It ... more

Doping (semiconductor)

In semiconductor production, doping intentionally introduces impurities into an extremely pure (also referred to as intrinsic) semiconductor for the ... more

Future value of a present sum

A time value of money calculation is one which solves for one of several variables in a financial problem. In a typical case, the variables might be: a ... more

Tractive Force

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

Bending moments at any point along the span of a uniformly loaded cantilevered beam

A cantilever is a beam anchored at only one end. The beam carries the load to the support where it is forced against by a moment and shear stress. A ... more

Turbine specific speed

The specific speed value (radian/second) for a turbine is the speed of a geometrically similar turbine which would produce one unit of the specific speed ... more

Knudsen number (Relationship to Mach and Reynolds numbers in gases)

The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. ... more

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