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Rayleigh number (for geophysical applications - related to bottom heating of the mantle from the core)

In fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or ... more

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

Stokes' law

Stokes’ law is an expression for the frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers (e.g., ... more

Liquid in a vertical tube (The height to which the column is lifted )

If a tube is sufficiently narrow and the liquid adhesion to its walls is sufficiently strong, surface tension can draw liquid up the tube in a phenomenon ... more

Bend allowance

Bending is a manufacturing process that produces a V-shape, U-shape, or channel shape along a straight axis in ductile materials, most commonly sheet ... more

Semi-Elliptic Laminated Leaf Spring (Stiffness)

Leaf spring, commonly used for the suspension in wheeled vehicles. The term is also used to refer to a bundled set of leaf springs. As the spring flexes, ... more

Stress-Optic Law

Photoelasticity is an experimental method to determine the stress distribution in a material.Unlike the analytical methods of stress determination, ... 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
Angle of elevation (for object following a ballistic trajectory)

A trajectory or flight path is the path that a moving object follows through space as a function of time. A trajectory can be described mathematically ... 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

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