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Conservation of Mechanical Energy

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Conservationof MechanicalEnergy

Boquilon, Shaira P.

Pulido, Rhea Angelie G.

Mendiola, Issiah Jeremiah L.

Cubillan, Kim Christian T.

Almeda, Angelica A.

Edradan, Gabrielle Ruth R.

Objects do not enter or leave a closed, isolated system. It is isolated from all external forces, and so no work can be done on it.

The law of conservation of energy states that ‘within a closed, isolated system, energy can change form but the total amount of energy is constant’. That is energy can be neither created nor destoyed.

To summarize, the conservation of energy is the total amount of energy in a system isolated from the rest of the universe always remains constant, although energy transformations from one form to another may occur within the system.

The Conservation of Energy is perhaps the most fundamental generalization in all science;

No violation of it has ever been found.

A ball alone, acted on by gravity, is not an isolated system, a ball on earth , however is an example of a closed, isolated system.

The kinetic energy of the ball can change, but the sum of gravitational potential and kinetic energy is constant.

The sum of potential and kinetic energy is often called mechanical energy.

Mathematically, the total energy in a given system is fixed. Just like this equation:

Total energy=Potential Energy + Potential Energy

Conservation of energy on a roller coaster ride means that the total amount of mechanical energy is the same at every location along the track. The amount of kinetic energy and the amount of potential energy is constantly changing. Yet the sum of the kinetic and potential energies is everywhere the same. This is illustrated in the diagram below. The total mechanical energy of the roller coaster car is a constant value of 40 000 Joules.

KEi + PEi + Wext = KEf + Pef

The equation illustrates that the total mechanical energy (KE + PE) of the object is changed as a result of work done by external forces. There are a host of other situations in which the only forces doing work are internal or conservative forces. In such situations, the total mechanical energy of the object is not changed. The external work term cancels from the above equation and mechanical energy is conserved. The previous equation is simplified to the following form:

KEi + PEi = KEf + PEf

Oscillation of a pendulum bob eventually will die away, and a bouncing ball finally comes to rest. Where did the mechanical energy go? Work was done against friction, and in the case of the ball, to change its shape when it bounces.The system was not isolated so its mechanical energy was not conserved.

When solving conservation of energy problems:

- Carefully identify the system. Make sure it is closed; no objects can leave or enter. It must also be isolated; no external forces can act on any object in the system. Thus, no work can be done on or by objects outside the system.
- Is friction present? If it is, then the sum of kinetic and potential energies will not be constant. But the sum of kinetic, potential and work done against friction will be constant.
- Finally, if there is no friction, find the initial and final total energies and set them equal.

The end!