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Volume thermal expansion coefficient

Thermal expansion is the tendency of matter to change in volume in response to a change in temperature through heat transfer. For a solid, we can ignore ... more

Cassie's Law

Cassie’s law describes the effective contact angle θc for a liquid on a composite surface. The law explains how simply roughing up a surface ... more

Fractional bandwidth (RLC circuits)

The bandwidth as a fraction of the resonance frequency. Bandwidth is the difference between the upper and lower frequencies in a continuous set of ... more

Dividend payout ratio

Dividend payout ratio is the fraction of net income a firm pays to its stockholders in dividends. The part of the earnings not paid to investors is left ... more

Buckling Coefficient

In science, buckling is a mathematical instability that leads to a failure mode.

When a structure is subjected to compressive stress, buckling may ... more

Energy Density (magnetic field)

Energy density is the amount of energy stored in a given system or region of space per unit volume or mass, though the latter is more accurately termed ... more

Metcalfe’s Law

Metcalfe’s law states that the value of a telecommunications network is proportional to the square of the number of connected users of the system ... 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.

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.


then we calculate the number of hours worked in the 20 years.


Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.


The efficiency is the resulting potential energy divided by the consumed energy.

Saturated Adiabatic Lapse Rate

The lapse rate is defined as the rate at which atmospheric temperature decreases with increase in altitude. The terminology arises from the word lapse in ... more

Mass fraction (relation between mass and molar concentration)

In chemistry, the mass concentration is defined as the mass of a constituent divided by the volume of the mixture. The mass concentration of a component ... more

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