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Elastic collision (final velocity of one of the two bodies in elastic collision)

An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total ... more

Terminal velocity (potato-shaped obgject)

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force ... more

Langarian point (radius around M2 in the absense of M1)

In celestial mechanics, the Lagrangian points (also Lagrange points, L-points, or libration points) are positions in an orbital configuration of two large ... more

Magnitude of proper motion

Proper motion is the astronomical measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the ... 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

Mean anomaly

In celestial mechanics, the mean anomaly is an angle used in calculating the position of a body in an elliptical orbit in the classical two-body problem. ... 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
Oloid enclosed Volume

An oloid is a three-dimensional curved geometric object that was discovered by Paul Schatz in 1929. It is the convex hull of a skeletal frame made by ... more

Perfectly inelastic collision

A collision is an isolated event in which two or more moving bodies (colliding bodies) exert forces on each other for a relatively short time. Collision is ... more

Difference between the maximum and the minimum height of a oloid

Oloid is the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies ... more

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