Relationship among Force, Power, Work and Energy
Force, work, energy and power are words used frequently in our everyday lives. What exactly do they mean? To put it simply, force is that which causes an object to move, while work is done when that force causes movement. Energy is the inherent ability of any object to do work, while power is the rate at which that work is done.
Law of Conservation of Mechanical Energy
Mechanical energy is stored in an object due to virtue of its motion. Potential energy and kinetic energy are the two types of mechanical energy, and the law of conservation of mechanical energy is associated with the conservation of these two energies in a system. Mechanical energy is basically a combination of potential and kinetic energy.
Principle of Conservation of Mechanical Energy
According to the law of conservation of mechanical energy, in an isolated system, that is, in the absence of non-conservative forces like friction, the initial total energy of the system equals to the total energy of the system. Simply stated, the total mechanical energy of a system is always constant (in case of absence of non-conservative forces). For instance, if a ball is rolled down a frictionless roller coaster, the initial and final energies remain constant. Conservative forces are those that don't depend on the path taken by an object. For example, gravity, spring and electrical forces are examples of mechanical energy.
Conservation of Mechanical Energy Equation
The quantitative relationship between work and energy is stated by the mechanical energy equation.
UT = Ki + Pi + Wext = Kf + Pf, where,
UT = Total mechanical energy
Ki = Initial kinetic energy
Kf = Final kinetic energy
Pi = Initial potential energy
Pf = Final potential energy
Wext = External work done
This is a general equation for mechanical energy conservation. In case, there are some