Lesson 8, Topic 1
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# Mechanical Energy Transformation | Law of Conservation of Energy

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Energy can be transformed from one form to another e.g. potential energy can be converted to kinetic energy and vice versa.

### Law of Conservation of Energy:

The law of conservation of energy states that in an isolated or closed system, the total energy remains constant or in other words, energy can neither be created nor destroyed, but it can be transformed from one form to another.

Electrical energy can be converted to heat energy and light energy. Mechanical energy can be converted to heat energy and chemical energy can be converted to food energy or light energy.

By an isolated system, we mean a group of objects that neither receives energy from or gives energy to objects outside the system.

### Potential and Kinetic Energy of a Falling Body:

For this topic let’s refer to kinetic energy asEk and potential energy as Ep

An object of mass m, held at point h, possesses maximum potential energy,Ep, and kinetic energy,Ek, is zero, because of no movement.

When the object is released, the kinetic energy,Ek, of the body increases, and the potential energy,Ep, decreases due to the decrease in height h. At the midpoint, the body possesses equal kinetic and potential energy i.e. Potential Energy = Kinetic Energy,Ep =Ek

Just before hitting the ground, the kinetic energy,Ek, is maximum while the potential energy,Ep, is zero. Hence, the transformation of potential energy,Ep, to Kinetic energy,Ek.

### Potential and Kinetic Energy of a Simple Pendulum:

In a simple pendulum with no friction, mechanical energy is conserved. When a simple pendulum oscillates with simple harmonic motion, it gains someÂ kinetic energyÂ because of this type of motion.

There is a constant exchange between kinetic and potential energy as the pendulum swings back and forth.

The motion of a pendulum is a classic example of mechanical energy conservation.

A simple pendulum consists of a mass, known as a bob, attached by a string, which is suspended from firm support.

As the pendulum moves, it sweeps out a circular arc, moving back and forth in a periodic fashion.Â

The pendulum swings from the highest point, C, through the centre of the swing, A, to the other highest point, B.

Total energy of the object at point C:

From the conservation law of energy,

Total energy = kinetic energy + potential energy

Total energy = Â½ x m x VÂ² + m x g x h

At point C v = 0, therefore the total energy = mgh

The energy at C is maximum potential energy which is at a height above A.

The Bob is at the lowest position at A, therefore the potential energy at that point is 0.

Also at A, the speed of the pendulum is maximum and so the kinetic energy is maximum at this point.

As the Bob moves from A to B, the kinetic energy at A is gradually transformed to potential energy, with potential energy becoming maximum at B.

At point B the total energy is potential energy and is equal to mgh.

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