Search results

Found 1006 matches
Monoclinic crystal system (Unit cell's volume)

In crystallography, the monoclinic crystal system is one of the seven lattice point groups. A crystal system is described by three vectors. In the ... more

Achromatic doublet (lens power)

An achromatic lens or achromat is a lens that is designed to limit the effects of chromatic and spherical aberration. Achromatic lenses are corrected to ... more

Radial Kepler equation

In orbital mechanics, Kepler’s equation relates various geometric properties of the orbit of a body subject to a central force.

It was first ... more

Interior perpendicular bisector of a triangle

The interior perpendicular bisector of a side of a triangle is the segment, falling entirely on and inside the triangle, of the line that perpendicularly ... more

Relation between internal bisectors of angles A, B, and C of a triangle and its sides

An angle bisector divides the angle into two angles with equal measures. An angle only has one bisector. Each point of an angle bisector is equidistant ... more

Miller indices calculator ( planar spacing distance in fcc system)

Miller indices form a notation system in crystallography for planes in crystal (Bravais) lattices.
In particular, a family of lattice planes is ... more

Vertical Wind Profile - Logarithmic Law

Wind speed extrapolation

In wind energy studies, two mathematical models or 'laws’ have generally been used to model the vertical profile of ... more

Worksheet 341

The aweÔÇÉinspiring 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.

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.


then we calculate the number of hours worked in the 20 years.


Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.


The efficiency is the resulting potential energy divided by the consumed energy.

Euler line (distance between the centroid and the circumcenter of a triangle)

In geometry, the Euler line is a line determined from any triangle that is not equilateral. It passes through several important points determined from the ... more

Cyclic quadrilateral (Ptolemy's theorem)

In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is ... more

...can't find what you're looking for?

Create a new formula