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Gravitational Potential (spherical symmetry)

Within a uniform spherical body of radius R and density ρ the gravitational force g inside the sphere varies linearly with distance r from the center, ... more

Gravity measurement with seconds pendulum (Kater's pendulum))

A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a ... 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
Green strain

A strain is a normalized measure of deformation representing the displacement between particles in the body relative to a reference length.The concept of ... more

Griffith's criterion in Linear elastic fracture mechanics (critical stress intensity factor)

Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid ... more

Hooke's law for continuous media

Hooke’s law states that the force needed to extend or compress a spring by some distance is proportional to that distance.The stresses and strains ... more

Horizontal 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 horizontal ... more

Horizontal 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 horizontal ... more

Ideal rocket equation (Tsiolkovsky rocket equation)

The Tsiolkovsky rocket equation, or ideal rocket equation describes the motion of vehicles that follow the basic principle of a rocket: a ... more

Impulse (Time)

Impulse is the product of a force and the time, for which it acts. The impulse of a force acting for a given time interval is equal to the change in linear ... more

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