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Velocity of a simple harmonic motion

A simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement. The motion is sinusoidal in ... more

Richardson Number - thermal convection

The Richardson number (Ri) is named after Lewis Fry Richardson (1881 – 1953). It is the dimensionless number that expresses the ratio of potential to ... more

Solid angle (in spherical coordinates)

In geometry, a solid angle is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the ... more

Law of Conservation of Linear Momentum - 3 particles example

In classical mechanics, linear momentum or translational momentum (pl. momenta; SI unit kg m/s, or equivalently, N s) is the product of the mass and ... more

Strain energy release (Irwin's modification for plane strain)

A fracture is the separation of an object or material into two, or more, pieces under the action of stress.There are three ways of applying a force to ... more

Inverse-square law gravitational field ( free-fall time for two point objects on a radial path)

Two objects in space orbiting each other in the absence of other forces are in free fall around each other. The motion of two objects moving radially ... 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
Curvature of a Bimetallic Beam

A bimetallic strip is used to convert a temperature change into mechanical displacement. The strip consists of two strips of different metals which expand ... more

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

Acceleration of reciprocating 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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