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Intensity - Mathematical description

In physics, intensity is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the ... more

Polar Moment of Area - Annulus Cross Section

The second moment of area, also known as moment of inertia of plane area, area moment of inertia, polar moment of area or second area moment, is a ... 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

Pick's theorem

Given a simple polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon’s vertices ... 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
Potential energy (electrostatic forces between two bodies)

Potential function for electrostatic forces between two bodies is the work required to move a charge from a point to any point in the electrostatic force ... more

Electric field (due to a point charge)

The electric field describes the electric force experienced by a motionless positively charged test particle at any point in space relative to the ... more

Free-fall time (radial trajectory of an ellipse with an eccentricity of 1 and semi-major axis R/2)

The free-fall time is the characteristic time that would take a body to collapse under its own gravitational attraction, if no other forces existed to ... more

Flux (as a single scalar)

Flux is two separate simple and ubiquitous concepts throughout physics and applied mathematics. Within a discipline, the term is generally used ... more

Bernoulli’s Equation (conservation of energy)

Bernoulli’s equation states that for an incompressible, frictionless fluid, the above mentioned sum is constant. If we follow a small volume of fluid along ... more

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