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Critical grain size (diameter)

Sediment transport is the movement of solid particles (sediment), typically due to a combination of gravity acting on the sediment, and/or the movement of ... more

Near branch of a hyperbola in polar coordinates with respect to a focal point

In mathematics, a hyperbola is a type of smooth curve, lying in a plane, defined by its geometric properties or by equations for which it is the solution ... more

Kepler's Third Law

In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

1.The orbit of a ... more

Centripetal(Centrifugal) Acceleration

Acceleration, in physics, is the rate of change of velocity of an object. An object’s acceleration is the net result of any and all forces acting on ... 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
Kepler's First Law

In astronomy, Kepler’s laws of planetary motion are three scientific laws describing the motion of planets around the Sun.

1.The orbit of a ... more

Reduced specific volume

In thermodynamicsIn thermodynamics, the reduced properties of a fluid are a set of state variables normalized by the fluid’s state properties at its ... more

Miller indices calculator (Case of cubic structures)

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

Steadily rotating crank ( displacement of the end of the connecting rod )

A crank is an arm attached at right angles to a rotating shaft by which reciprocating motion is imparted to or received from the shaft. It is used to ... more

Torque to lower a load (by lead screw-related to the coefficient of friction))

A leadscrew (or lead screw), also known as a power screw or translation screw, is a screw used as a linkage in a machine, to translate turning motion into ... more

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