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Angle required to hit polar coordinate (x,y) - (projectile following a ballistic trajectory)

In physics, the ballistic trajectory of a projectile is the path that a thrown or launched projectile or missile without propulsion will take under the ... more

Self-buckling critical height ( for a free-standing, vertical column)

Column or pillar in architecture and structural engineering is a structural element that transmits, through compression, the weight of the structure above ... 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
Hydrostatic Pressure - simplified version

In a fluid at rest, all frictional stresses vanish and the state of stress of the system is called hydrostatic.For water and other liquids, this integral ... more

Total Leverage

In finance, leverage is a general term for any technique to multiply gains and losses. Financial leverage tries to estimate the percentage change in net ... more

Water Rocket - peak height

A water rocket is a type of model rocket using water as its reaction mass. Such a rocket is typically made from a used plastic soft drink bottle. The water ... more

Solute flux (Forward osmosis)

Forward osmosis (FO) is an osmotic process that, like reverse osmosis (RO), uses a semi-permeable membrane to effect separation of water from dissolved ... more

Darcy friction factor - Swamee–Jain equation

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used ... more

Evaporation - Penman Equation (Shuttleworth modification)

The Penman equation describes evaporation (E) from an open water surface, and was developed by Howard Penman in 1948. Penman’s equation requires ... more

Orbit Equation

In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. ... more

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