The power of gratitude

Potential energy is not just a property of each object, but also a property of the interactions between objects in a chosen system. For each type of interaction present in a system, there is a corresponding type of potential energy. The total potential energy of the system is the sum of the potential energies of all the objects. Potential energy can be classified into two major categories: gravitational potential energy and elastic potential energy. The potential energy associated with a...

Since gravitational force is a conservative force, the amount of work done to move an object between two points in the gravitational field in which it resides is independent of the path taken. Thus, similar to the gravitational field, a gravitational potential energy function can be defined, which depends only on spatial coordinates.
Consider a mass gravitationally bound to another object. For example, the Earth is gravitationally bound to the Sun’s gravitational field. The potential...

Consider a circuit with two sinusoidal voltage sources. Each one influences the circuit independently, and the superposition principle helps us understand the combined effect by adding up the responses from each source.

Consider a system comprising several point masses. The coordinates of the center of mass for this system can be expressed as the summation of the product of each mass and its position vector divided by the total mass:

The concept of work involves force and displacement; meanwhile, the work-energy theorem relates the net work done on a body to the difference in its kinetic energy, calculated between two points on its trajectory. While none of these quantities or relations involves time explicitly, we know that the time available to accomplish work is often just as important as the amount of work itself. For example, sprinters in a race may have achieved the same velocity at the finish, therefore,...

Graded potentials are localized fluctuations in the cell membrane's electrical charge, commonly found in the dendrites of neurons. The magnitude of these potential changes depends on the strength of the initiating stimulus. In a membrane at its resting potential, a graded potential signifies a voltage shift either above -70 mV or below -70 mV.
Graded potentials fall into two categories: depolarizing and hyperpolarizing. Depolarizing graded potentials typically occur when sodium (Na+) or...