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Fresnel reflection (Reflectivity Rs)

The Fresnel equations (or Fresnel conditions) describe the behaviour of light when moving between media of differing refractive indices. The reflection of ... more

Fresnel reflection (Reflectivity Rp)

The Fresnel equations (or Fresnel conditions) describe the behaviour of light when moving between media of differing refractive indices. The reflection of ... 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

4th Equation of Motion for Rotation - Angular Velocity : time independent

In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... more

Vertical Curve - Offset

Offsets are vertical distances from the initial tangent to the curve, play a significant role in vertical curve design.

Vertical Curves are the ... more

2nd Equation of Motion for Rotation - Final Angle

In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of ... 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
Orbital Eccentricity - gravitational force

The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect ... more

Cycloid ( parametric equation Y-coordinate)

A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a ... more

Cycloid ( parametric equation X- coordinate)

A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage. It is an example of a ... more

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