All matter contains one form of energy or another. Matter by definition is anything that occupies space and has weight (Nave, 2012). According to Nave, all matter, when subjected to act by an external force changes from one form of energy to another. Kinetic energy is defined as the energy possessed by a body in motion (Nave). A body is termed as having potential energy by virtue of its motion (Niemi, 2000; Marjanovic & Milkovic, 2010; Jones, 2012).
Take for example, a boy with a huge ball (mass m) at the top of a hill (see figure below). While the ball is at the top of the hill, it contains potential energy since it is assumed to be at rest while in that position. The boy then gives the ball a shove (force F) such that the ball starts rolling down the hill. In this case, the ball starts accelerating downhill due to its mass in addition to the force used by the boy, and accelerated by contributions of the gravitation force. As the ball starts rolling downhill, the potential energy initially possessed by the ball is converted into kinetic energy (energy in motion).
Consider such a scenario in which the speed of a point mass m is much less than that of light, it therefore means that the kinetic energy of that point mass m is given by the following equation where m is mass and v is speed/ velocity.
In this case, it is assumed that the speed is comparable with c (speed of light) thus; its relativistic kinetic energy expression above is applicable (Marjanovic & Milkovic, 2010). In this case, m is the mass of the object (Marjanovic & Milkovic, 2010). Mass by definition is the fundamental property of any object (Niemi, 2000). To some, mass is defined as the numerical measure of the inertia that an object possesses (Marjanovic & Milkovic, 2010). Mass can also be defined as the fundamental measure of the quantity or amount of matter within the object under consideration (Jones, 2012).
Velocity v in the expression is the direction of movement by an object (Jones, 2012). Velocity is a vector quantity; thus, the object is assumed to be moving in a linear direction (Jones, 2012). Consider the picture adjacent, the cheetah possesses kinetic energy given that it is in motion. Its motion is made possible by its body mass and the speed at which it travels.
In other words, kinetic energy is an expression whose purpose is to show that a moving object can and do work on anything they come into contact (Marjanovic & Milkovic, 2010). In essence, kinetic energy quantifies the amount of work that an object does accentuated by its motion (Marjanovic & Milkovic, 2010). Take another scenario in which a moving track that is heavily laden approaches at a high speed. In this case, if a pedestrian decides to cross the road in front of the track and they come into contact, the damage on the individual will be subject to the mass of the moving car accentuated by the speed at which this track was moving. For a slow moving track, the damage might be manageable but for a speeding track, there is a higher likelihood that fatalities will result. In terms of work and energy, the fast moving track with have more work on the pedestrian as compared to a slow moving track's work in a similar pedestrian given the same mass.
Work is deemed to have been done on an object in the event that a force acts on the object in the direction of the motion or the force has a component that is an addition in the direction of the motion (Nave, 2012). However, it is imperative to delineate the fact that there is no work done in the event that there is no motion on the object/ mass, neither is there motion in the event that the force acting on the object is perpendicular to the motion of the object (Nave, 2012). Niemi (2000) and Nave (2012) posits that all energy can be in either one of the existent two states, which are either kinetic energy, or potential energy. Additionally, energy can be transferred from one form to another (Fowler, 2007). For example, potential energy can be transferred to kinetic energy as well as energy being transferred between objects (Niemi, 2000; Fowler, 2007).
According to Nave (2012), an object has the capability to do work by virtue of its position in a gravitational field (thus gravitational potential energy) or as a result of its position in an electric field (thus electric potential energy). There is also the possibility of an object to be able to do work by virtue of its position in a magnetic field (thus magnetic potential energy) or its position by virtue of an elastic deformation or on a stretched spring (thus elastic potential energy) (Nave, 2012). Consider the example (figure) below. In this figure, the ball, while at the top of the sliding grid (ruler) possesses potential energy. However, the work of gravitational force and the elevation makes it possible for conversion of potential energy into kinetic energy. Upon reaching at the foot of the ruler, the kinetic energy gradually gets converted into potential energy and the ball comes to rest some distance from the bottom of the ruler.
At this juncture, it is vital to connote that the sum of potential energy and kinetic energy make up mechanical energy (Nave, 2012).
For an isolated system, the total energy of such a system is subject to the principle of conservation of energy (Nave, 2012). It is widely acknowledged that in the event that a given system does not interact with its immediate environment in any identifiable manner, it thus does mean that certain mechanical properties within that system remain unchanged (Nave 2012). That is to say, they are constants of motion and are thus considered to be conserved. This means that the conservation laws are applicable, which are the fundamental principles of mechanics (Marjanovic & Milkovic, 2010). According to Nave (2012), Marjanovic & Milkovic (2010), Jones (2012) and Niemi (2000), energy can neither be created nor destroyed. This means that given that energy can neither be created nor destroyed, it can only be converted from one form to the next based on prevailing conditions that enable such conversions. This principle of conservation of energy is obeyed on a wide range of application ranging from the works of Einstein’s Caveat () to a powerful tool for mechanics problem solving in which external forces obey the work-energy principle (Nave, 2012).
It would be prudent to also define an isolated system as a collection of matter that never interacts with the rest of its environment or universe (Marjanovic & Milkovic, 2010; Nave 2012). Nevertheless, such a system does not exist. The problem with this is the fact that there exist no shied on any system that will guard a system against gravity while the electromagnetic force has an infinite range (Nave, 2012).
Consider the system adjacent. The gravitational force pulls particles downwards forcing the arrows to face downward while the pistons and cylinders at the top to shift positions downwards. This movement is best viewed using Open Office Software like Apache Open Office TM or Libre Open Office TM. When the force (piston on the lower side) pushes up, the arrangement of the arrows change to face in the upward direction. In this case, the top cylindrical circles stick to the roof of the main container. This depiction shows magnetic polarization and the effect that change in polarity has on dipoles. To the right of the figure is a metric system that calculates energy changes with respect to change in piston movement. However, it is interesting to note that, irrespective of the direction that the dipoles adopt, the amount of energy remains positive. This supports earlier posit on the principle of conservation of energy. No new energy is created neither is there any energy that is destroyed rather the energy is converted from one form to another.
For an object with a finite size, such an object’s kinetic energy is termed as translational kinetic energy of that mass so that it is distinguished from any form of rotational kinetic energy (Nave, 2012) that such an object might possess. For such an object, its total kinetic energy is a summation of the object’s translational kinetic energy of its center of mass and its kinetic energy of rotation about the center of that mass (Nave, 2012).
Derivation of kinetic energy
Assuming that the mass was at rest prior to the force being applied, it thus does imply that thus
Consider the definition of force from Newton’s law of motion, where m is mass and a is acceleration.
Acceleration is given as final velocity in unit time.
Earlier on there was mention of gravitational potential energy although the subject was not exemplified then. Consider a scenario in which work is done against the gravity (Huang & Xingze, 2006). Take for example; climbing staircases or lifting an object from the ground, in both cases, work is done against the gravity. When there is work done, there is imperatively transformation of energy from one form to the next (Huang & Xingze, 2006).
The change in gravitational potential energy between translation between points A and B is independent of the path adopted/ taken (Huang & Xingze, 2006). Take for example; in the adjacent figure, two individuals take two independent paths. One opts to take meandering staircase while the other opts to use other machines (a pulley in this case) to lift the object from point A to point B (Huang & Xingze). An interesting phenomenon about gravity is the fact that it falls under a small class of forces in which their contribution to the work done can be either for or against the force applied depending on the inception and finishing point of the movement (Huang & Xingze). In this case, the objects are on transit from the ground to a height h. By mathematical definition, change in potential energy is given by a product of mass (m), gravitational acceleration (a) and height (h). Therefore, since the objects are working against the gravitational force, g will have a negative effect (that is -g). Therefore, gravitational potential energy will be given as.
In this case, the kinetic energy of the system will be lost as the object (plus the carrier) move from point A to point B (Huang & Xingze). That is. Since work is done against the gravity, for the individual lifting the object m using a pulley, assuming that the object is relatively heavy, if the rope were to snap, the lost kinetic energy will be regained and an impact on the lifter may be detrimental based on the height of the object prior to snapping.
In conclusion, kinetic energy is the energy in motion. In simple terms, kinetic energy is the best exemplification that an object in motion can do work. When an object/ mass in motion come to rest, the kinetic energy changes to potential energy defined as energy possessed by an object by virtue of its position. In the event that an object is moving towards or against the gravity at its resting position, the object is termed as possessing gravitational potential energy. Kinetic energy and its related technology have diverse applications including electromagnetic platform, pulleys, gears, web animation and animatronics among others.
Fowler, M. (2007). Working with gravity: Potential energy. Retrieved from http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/GravPotEnergy.pdf
Huang, R. X., & Xingze, J. (2006). Gravitational potential energy for the thermal circulation in a model ocean. Journal of Physical Oceanography, 36, 1420-1429. Doi: http://dx.doi.org/10.1175/JPO2914.1
Jones, A. Z. (2012). What is kinetic energy? Education Physics. Retrieved from http://physics.about.com/od/energyworkpower/f/KineticEnergy.htm
Marjanovic, J., & Milkovic, V. (2010). Kinetic energy and over unity. Veljko Milkovic Research & Development Center: Novi Sad, Serbia. Retrieved from http://www.veljkomilkovic.com/Docs/Jovan_Marjanovic_Veljko_Milkovic_Kinetic_Energy_and_Overunity.pdf
Nave, R. (2012). Mechanics. Hyper Physics.
Niemi, M. (2000). Kinetic energy: How to add some motion to your web pages using DHTML in GoLive. Adobe Magazine, 43-46. Retrieved from http://www.adobe.com/products/adobemag/archive/pdfs/0003htmn.pdf