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Mach wave (angle)

In fluid dynamics, a Mach wave is a pressure wave traveling with the speed of sound caused by a slight change of pressure added to a compressible flow. ... more

Terminal velocity (under buoyancy force)

The terminal velocity of a falling object is the velocity of the object when the sum of the drag force and buoyancy equals the downward force of gravity ... more

Damping ratio ( related to damping coefficients)

Linear damping occurs when a potentially oscillatory variable is damped by an influence that opposes changes in it, in direct proportion to the ... more

Mechanical Advantage - Differential Pulley

Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves ... more

Prandtl–Meyer expansion fan - turn angle

A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, is a centred expansion process that occurs when a supersonic flow turns ... 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
Prandtl–Meyer expansion fan - first Mach line angle

A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, is a centred expansion process that occurs when a supersonic flow turns ... more

Prandtl–Meyer expansion fan - last Mach line angle

A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, is a centred expansion process that occurs when a supersonic flow turns ... more

Terminal velocity (potato-shaped obgject)

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force ... more

Terminal Velocity (without considering buoyancy)

Terminal velocity is simply the fastest speed that a falling object can reach in a certain circumstance. Different objects have different terminal ... more

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