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Surface Tension - surface area growth : force

Surface tension is a contractive tendency of the surface of a liquid that allows it to resist an external force. Surface tension is an important property ... more

Linear charge density

Linear density is the measure of a quantity of any characteristic value per unit of length. Llinear charge density (the amount of electric charge per unit ... more

Strain energy release (Irwin's modification for plane strain)

A fracture is the separation of an object or material into two, or more, pieces under the action of stress.There are three ways of applying a force to ... more

Cost variance (CV)

Earned value management (EVM), earned value project management, or earned value performance management (... more

The power to thrust ratio - rocket propulsion

Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with ... more

Distance between two points (two-space)

Distance is a numerical description of how far apart objects are. In analytic geometry, the distance between two points of the xy-plane can be found using ... 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
Number density (Relation to Mass density)

Number density is an intensive quantity used to describe the degree of concentration of countable objects. For atoms or molecules of a well-defined ... more

Mean anomaly - function of mean longitude

In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. ... more

Descartes' theorem ( externally tangent circle to three given kissing circles)

In geometry, Descartes’ theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain ... more

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