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Settling velocity (Stokes law)

Stokes’ law can be used to calculate the viscosity of a fluid. Stokes’ law is also important in the study for Viscous Drag , Terminal Velocity ... more

X-Coordinate of the involute of a circle

An involute (also known as evolvent) is a curve obtained from another given curve by attaching an imaginary taut string to the given curve and tracing its ... more

Critical Speed of a Rotating Shaft - Dunkerley's method

In solid mechanics, in the field of rotordynamics, the critical speed is the theoretical angular velocity that excites the natural frequency of a rotating ... more

Y-Coordinate of the involute of a circle

An involute (also known as evolvent) is a curve obtained from another given curve by attaching an imaginary taut string to the given curve and tracing its ... 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
Thermal de Broglie wavelength (Massless particles)

The thermal de Broglie wavelength is the average de Broglie wavelength of the gas particles in an ideal gas at the specified temperature. We can take the ... more

Apsis - Periapsis minimum distance

An apsis, plural apsidesis a point of greatest or least distance of a body in an elliptic orbit about a larger body. For a body orbiting the Sun the ... more

Apsis - Apoapsis maximum distance

An apsis, plural apsidesis a point of greatest or least distance of a body in an elliptic orbit about a larger body. For a body orbiting the Sun the ... more

Dynamic (shear) viscosity

The dynamic (shear) viscosity of a fluid expresses its resistance to shearing flows, where adjacent layers move parallel to each other with different ... more

Arithmetic Standard Deviation - 2nd moment

Shows how much variation or dispersion from the average exists, on the particles’ size distribution of a soil, in metric scale. Arithmetic mean size (1st ... more

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