state & explain the law of conservation of energy with an example 2. explain how total energy a swinging pendulam at any instant of time remains conserved illustrate your answer with the help of Lbelled diagram

1) Combustion of fuel results in the conversion of chemical energy into the heat energy

2) Kinetic energy of the falling water is converted to the electrical energy (hydroelectricity)

In case of a simple pendulum, let us consider that a small ball of mass

*m*is executing simple harmonic motion as shown below,

Suppose

*N*is an arbitrary point from where the ball stops and again get back into it’s to and fro motion. Therefore, at point

*N*, the kinetic energy of the ball is zero because the ball is at rest at this position so,

$K{E}_{N}=0$

Let at point

*N*, the height of the ball is

*h*from the ground. Hence, due to gravity, the ball will possesses potential energy as,

$P{E}_{N}=mgh$

Thus at point

*N*, the total mechanical energy

*E*which is sum of potential energy and the kinetic will become,

${E}_{N}=mgh+0\phantom{\rule{0ex}{0ex}}{E}_{N}=mgh$

Again consider another point

*L*in the air during the to and fro motion of the ball such that the distance of point

*L*from the ground is also

*h*. Here at point

*L*, the kinetic energy of the ball is zero because the ball is at rest at this point, that is,

$K{E}_{L}=0$

At point L, the potential energy is given as,

$P{E}_{L}=mgh$

Hence, again the total mechanical energy at point

*L*will become,

${E}_{L}=mgh$

Consider a point

*M*where the velocity of the ball will be maximum but the height will be almost zero. Thus, at this point the gravitational potential energy of the ball becomes zero,

$P{E}_{M}=0$

However, the kinetic energy of the ball at point

*M*will become,

$K{E}_{M}=\frac{1}{2}m{{v}_{max}}^{2}$

Thus at point

*M*, the total mechanical energy will be,

${E}_{M}=0+\frac{1}{2}m{{v}_{max}}^{2}\phantom{\rule{0ex}{0ex}}{E}_{M}=\frac{1}{2}m{{v}_{max}}^{2}$

Hence from the above result we can say that the potential energy of the ball is completely transformed into the kinetic energy of the ball during SHM.

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