On the shoulders of (real) giants

Archimedes' principle states that an upward buoyant force exerted on a body that is immersed partially or entirely in a fluid is equal to the weight of the fluid displaced by it. To understand how much buoyant force is needed to make an object float, let us think about what happens when a submerged object is removed from a fluid. If the object were not in the fluid, the space occupied by the object would be filled by the fluid having a weight wfl. This weight is supported by the surrounding...

Our everyday observation tells us that all objects close to the Earth naturally tend to fall to the ground. Early philosophers assumed that this downward force was unique to Earth. By the 16th century, Nicolaus Copernicus (1473-1543) put forward the heliocentric theory, which suggested that Earth and other planets orbited the sun, while the Moon orbited the Earth. However, it was Isaac Newton (1642-1727) who linked these two motions together in the 17th century. He reasoned that the force of...

Designing columns to withstand eccentric loads is a critical aspect of structural engineering, ensuring structures can support off-center loads without failure. This design process must account for the additional normal stresses introduced by eccentric loading, which can significantly influence a column's stress distribution and overall stability. An eccentric load applied to a column induces normal stresses that can be conceptualized as a combination of stresses due to an equivalent centric...

Internal forces and the center of gravity are fundamental concepts in mechanics, playing a crucial role in understanding the behavior and stability of structures and objects under various conditions. A comprehensive understanding of these principles is essential for engineers, architects, and designers to create safe and efficient systems.
Internal forces are generated within a body due to the interaction between its particles. These forces can be categorized into tension, compression, and...

Newton's third law states that every action has an equal and opposite reaction. Consider a swimmer pushing off the side of a pool. They push against the wall of the pool with their feet and accelerate in the direction opposite to that of their push. This occurs because the wall exerts an equal and opposite force on the swimmer. Here, the forces do not cancel out each other as they are acting on different systems. In this case, there are two systems: the swimmer and the wall. If we select the...

Sir Isaac Newton established the universality of the law of gravitational attraction based on empirical evidence and inductive reasoning. He published his work in Philosophiae Naturalis Principia Mathematica ("the Principia") on July 5, 1687.
Newton's law of gravitational attraction is a fundamental law of physics that governs the attraction between objects. It states that the magnitude of the gravitational force between any two objects is proportional to their masses and inversely proportional...