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Dalton's law - mole fraction

Dalton’s law (also called Dalton’s law of partial pressures) states that in a mixture of non-reacting gases, the total pressure exerted is ... more

Speed of Sound (air, ideal gases) - relative to molar mass

The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of the speed of sound is the ... more

Gay-Lussac's Law (Pressure-temperature law)

The pressure of a gas of fixed mass and fixed volume is directly proportional to the gas’ absolute temperature. If a gas’s temperature ... more

Vertical Forces at the wheels for a bicycle (rear wheel)

Though longitudinally stable when stationary, a bike may become longitudinally unstable under sufficient acceleration or deceleration. The normal ... more

Vertical Forces at the wheels for a bicycle (front wheel)

Though longitudinally stable when stationary, a bike may become longitudinally unstable under sufficient acceleration or deceleration. The normal ... 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
Tsiolkovsky rocket equation - acceleration based

The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that ... more

Speed of Sound (air, ideal gases) - relative to the mass of a single molecule

The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of the speed of sound is the ... more

Porosity

The volume of the voids of a soil over the total volume of the sample defines the porosity of a soil. Used in geology, hydrogeology, soil science, and ... more

Anelastic Attenuation Factor

In reflection seismology, the anelastic attenuation factor, often expressed as seismic quality factor or Q (which is inversely proportional to attenuation ... more

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