In 1653, the French philosopher and scientist Blaise Pascal published "Treatise on the Equilibrium of Liquids," which discussed the principles of static fluids. A static fluid is a fluid that is not in motion. When a fluid is not flowing, we say that the fluid is in static equilibrium. If the fluid is water, we say it is in hydrostatic equilibrium. For a fluid in static equilibrium, the net force on any part of the fluid must be zero; otherwise, the fluid will start to flow. Pascal...

The direction in which the induced emf drives the current around a wire loop can be found through the negative sign. However, it is usually easier to determine this direction with Lenz's law, named in honor of its discoverer, Heinrich Lenz (1804–1865). Lenz's law states that the direction of the induced emf drives the current around a wire loop always to oppose the change in magnetic flux that causes the emf.
If a bar magnet is moved toward a coil such that the magnetic flux...

Pascal's experimentally proven observations—that a change in pressure applied to an enclosed fluid is transmitted undiminished throughout the fluid and to the walls of its container—provide the foundations for hydraulics, one of the most important developments in modern mechanical technology.
Hydraulic systems are used to operate automotive brakes, hydraulic jacks, and numerous other mechanical systems. We can derive a relationship between the forces in a simple hydraulic system...

Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.

Resistors are fundamental components in electrical circuits, often manufactured from metallic alloys or carbon compounds. They model a material's ability to resist the flow of electric current, a characteristic that is crucial in controlling and regulating electrical power within a circuit.
This current-resisting behavior of resistors is governed by Ohm's law, which states that the voltage across a resistor is directly proportional to the current flowing through it.

Many materials exhibit a simple relationship between the values of current, voltage, and resistance, known as Ohm’s law. The current that flows through most substances is directly proportional to the voltage applied to them. The German physicist Georg Simon Ohm (1787–1854) was the first to demonstrate experimentally that the current in a metal wire is directly proportional to the voltage applied. Any material, component, or device that obeys Ohm’s law, where the current...