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Hot Air Balloon Lift

The hot air balloon is the oldest successful human-carrying flight technology. The first hot-air balloon flown in the United States was launched from the ... more

Power - rotational systems (torque)

Power is the rate at which work is done. It is equivalent to an amount of energy consumed per unit time. Power in mechanical systems is the combination of ... more

Vis-Viva Equation

In astrodynamics, the vis viva equation, also referred to as orbital energy conservation equation, is one of the fundamental equations that govern the ... more

Vis-Viva Equation with standard gravitational parameter

In astrodynamics, the vis viva equation, also referred to as orbital energy conservation equation, is one of the fundamental equations that govern the ... more

Albedo - correlation with Absolute Magnitude and Diameter

Albedo (/ælˈbiːdoʊ/), or reflection coefficient, derived from Latin albedo “whiteness” (or reflected sunlight) in turn from albus ... 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
Apparent power

The power factor of an AC electrical power system is defined as the ratio of the real power flowing to the load, to the apparent power in the circuit. In a ... more

Boltzmann distribution in mechanics

In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution, probability measure, or ... more

Boltzmann factor in mechanics

In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution, probability measure, or ... more

Hawking Radiation - Temperature of a black body (or a black hole)

A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A black hole ... more

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