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Magnetic dipole moment (Ampère model)

Far away from a magnet, its magnetic field is almost always described (to a good approximation) by a dipole field characterized by its total magnetic ... more

Moment of Inertia - I-Beam (Ideal cross section)

An I-beam, also known as H-beam, W-beam (for “wide flange”), Universal Beam (UB), Rolled Steel Joist (RSJ), or ... more

Cantilever Euler Beam - Maximum Displacement

Euler–Bernoulli beam theory (also known as engineer’s beam theory or classical beam theory) is a simplification of the linear theory of elasticity ... more

Auger electron spectroscopy - emitted electron kinetic energy

Auger electron spectroscopy is a common analytical technique used specifically in the study of surfaces and, more generally, in the area of materials ... more

Wind Power - Betz's law

Wind power is the conversion of wind energy into a useful form of energy, such as using wind turbines to produce electrical power, windmills for mechanical ... more

Allowable Strength Design Load combination (eq3)

In structural engineering, a structure is a body or combination of pieces of rigid bodies in space to form a fitness system for supporting loads. ... more

Schwarzschild radius

The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is the radius of a sphere such that, if all the ... more

Auger electron spectroscopy - Total yield

Auger electron spectroscopy is a common analytical technique used specifically in the study of surfaces and, more generally, in the area of materials ... 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
Velocity of the reciprocating motion of the piston with respect to crank angle

A piston is the moving component that is contained by a cylinder and is made gas-tight by piston rings. In an engine, its purpose is to transfer force from ... more

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