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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

Potential energy

Potential energy is the energy of a body or a system with respect to the position of the body or the arrangement of the particles of the system. The amount ... more

Entropy of isobaric process

An isobaric process is a thermodynamic process in which the pressure stays constant: ΔP = 0. The heat transferred to the system does work, but also changes ... more

Carnot cycle

Every single thermodynamic system exists in a particular state. When a system is taken through a series of different states and finally returned to 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
Elastic Potential Energy

According to Hooke’s Law, Elastic potential energy is stored in a simple harmonic oscillator at position x,for example, the energy saved in an object ... more

Kinetic energy (related to object's momentum)

In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is the work needed to accelerate a body of a given mass ... more

Escape Velocity

Escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero. It is the speed needed to ... more

Energy–Maneuverability Theory (aircraft performance)

Energy–maneuverability theory is a model of aircraft performance. It was developed by Col. John Boyd, and is useful in describing an aircraft’s ... more

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