The universe is composed of matter in different forms, and all forms of matter contain energy.  The different forms of energy on Earth originate from the Sun—the ultimate energy source. For instance, plants capture light energy from the Sun, and through the process of photosynthesis, convert it into chemical energy. This stored energy from plants can be harnessed in many ways. For example, eating plant products as food provides energy for our body to function, and burning wood or...

The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the interpretation of the dynamics of the system becomes even simpler.
Take the example of a skater on a parabolic ramp. The potential energy at different points along the ramp will be proportional to the height of the ramp, which varies quadratically with the horizontal position on the ramp. As the skater moves down the ramp from the highest position,...

Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the system.
The point in the energy diagram at which the system’s potential energy is the lowest is known as the local minima. The system tends to stay in this position indefinitely unless acted upon by a net force. The slope of the potential energy diagram at the local minima is zero, indicating that zero net force is acting on the system. The...

Open channel flow, where a fluid flows with a free surface exposed to the atmosphere, is primarily governed by gravitational and surface effects, distinguishing it from closed conduit or pipe flow. In open channels such as rivers, canals, and artificial channels, energy analysis provides valuable insights into flow behavior and the relationship between depth, velocity, and slope.Specific Energy and Flow DepthIn open channel flow, the specific energy, E, combines the gravitational potential...

A decreasing function describes a relationship where the output consistently declines as the input increases. This means that for any two input values, if one is greater than the other, the corresponding output is smaller. Mathematically, a function f is decreasing on an interval I if for every x1 < x2​ in I, f (x1) > f (x2). This type of behavior is visually identified on a graph that slopes downward from left to right.The nature of a function can be analyzed by calculating...

Trophic level transfer efficiency (TLTE) is a measure of the total energy transfer from one trophic level to the next. Due to extensive energy loss as metabolic heat, an average of only 10% of the original energy obtained is passed on to the next level. This pattern of energy loss severely limits the possible number of trophic levels in a food chain.