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Thrust-to-Weight Ratio

Thrust-to-weight ratio (TWR) is a dimensionless ratio of thrust to weight of a rocket, jet engine, propeller engine, or a vehicle ... more

Ball Screw - Tensile Compressive Load

A ball screw is a mechanical linear actuator that translates rotational motion to linear motion with little friction. A threaded shaft provides a helical ... more

Solar Rotation

Solar rotation is able to vary with latitude because the Sun is composed of a gaseous plasma. The rate of rotation is observed to be fastest at the equator ... more

Volume of a hollow sphere

Calculates the volume of a hollow sphere. A sphere is a perfectly round geometrical and circular object in three-dimensional space that resembles the shape ... more

Minimum railway curve radius

The minimum railway curve radius, the shortest allowable design radius for railway tracks under a particular set of conditions. It has an important bearing ... more

Thrust-to-Weight Ratio - Propeller-driven aircraft

Thrust-to-weight ratio (TWR) is a dimensionless ratio of thrust to weight of a rocket, jet engine, propeller engine, or a vehicle ... more

Critical point of a cubic function ( local maximum )

A cubic function is a function of the form f(x): ax3 + bx2 + cx + d.
The critical points of a cubic equation are those values of x where the slope of ... more

Critical point of a cubic function ( local minimum )

A cubic function is a function of the form f(x): ax3 + bx2 + cx + d.
The critical points of a cubic equation are those values of x where the slope of ... 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
Variance of the sample kurtosis of a sample of size n

In statistics and quantitative research methodology, a data sample is a set of data collected and/or selected from a statistical population by a defined ... more

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