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Perimeter of a Regular polygon

A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may ... more

Frequency (Doppler effect for a moving black body)

Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by ... more

Slip factor

In turbomachinery, the slip factor is a measure of the fluid slip in the impeller of a compressor or a turbine, mostly a centrifugal machine. Fluid slip is ... more

Speed of sound in three-dimensional solids (pressure waves)

The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium. Sound travels faster in liquids and ... more

Horizontal curve - Sight obstraction distance (S>L)

Horizontal Curves are one of the two important transition elements in geometric design for highways (along with Vertical Curves). A horizontal curve ... 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
Speed of Sound in Fluids (Newton-Laplace equation )

The speed of sound is the distance travelled per unit of time by a sound wave propagating through an elastic medium.
Sound travels faster in liquids ... more

Vertical Curve - Stopping Sight Distance

Sight distance is dependent on the type of curve used and the design speed. For crest curves, sight distance is limited by the curve itself, as the curve ... more

Doppler Effect Wavelength Front

Doppler Effect is the change in frequency and wavelength of a wave for an observer moving relative to the source of the waves. Compared to the emitted ... more

1st Equation of Motion for Rotation - Angular Velocity

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

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