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Arrhenius number

In chemical kinetics, the pre-exponential factor or A factor is the pre-exponential constant in the Arrhenius equation. Here named as Arrhenius number.

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Cycloid (Cartesian equation)

A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a ... more

Archie's Law

In petrophysics, Archie’s law relates the in-situ electrical conductivity of a sedimentary rock to its porosity and brine saturation as shown ... more

Stokes's Law of Sound Attenuation

Stokes’s law of sound attenuation is a formula for the attenuation of sound in a Newtonian fluid, such as water or air, due to the fluid’s ... more

Karman vortex street formula

In fluid dynamics, a Kármán vortex street is a repeating pattern of swirling vortices caused by the unsteady separation of flow of a fluid around blunt ... more

Simple Pendulum (Period)

Simple Pendulum is a mass (or bob) on the end of a weightless string, which, when initially displaced, will swing back and forth under the influence of ... more

Linear damping oscillation

Damped harmonic motion is a real oscillation, in which an object is hanging on a spring. Because of the existence of internal friction and air resistance, ... 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
Mutual inductance factor

The mutual inductance factor depends on the number of turns each coil and the permeance of the space occupied by the flux

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Ball Screw - Preload Drag Torque

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

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