

LAW
OF CONSERVATION OF ENERGY


According
to the law of conservation of energy : "Energy can neither be created nor it is destroyed, however energy can be converted from one form energy to any other form of energy" 

SHOW
THAT THE MOTION OF A SIMPLE PENDULUM IS ACCORDING TO THE LAW OF CONSERVATION
ENERGY. OR PROVE THE LAW OF CONSERVATION WITH THE HELP OF A SUITABLE EXAMPLE. 


We
know that the motion of the bob of a simple pendulum is simple harmonic
motion. Here we have to prove that the energy is conversed during the motion
of pendulum. Proof: Consider a simple pendulum as shown in the diagram. 

Energy
Conservation At Point ‘A’


At
point ‘A’ velocity of the bob of simple pendulum is zero. Therefore, K.E.
at point ‘A’ = 0. Since the bob is at a height (h), Therefore, P.E. of the
bob will be maximum. i.e. P.E. = mgh. Energy total = K.E. + P.E Energy total = 0 + mgh Energy total = mgh This shows that at point A total energy is potential energy. 

Energy
Conservation At Point ‘M’


If
we release the bob of pendulum from point ‘A’, velocity of bob gradually
increases, but the height of bob will decreases from point to the point.
At point ‘M’ velocity will become maximum and the height will be nearly
equal to zero. Thus , K.E. = maximum = 1/2mV^{2} but P.E. = 0. Energy total = K.E. + P.E Energy total = 1/2mV^{2} + 0 Energy total = 1/2mV^{2} This shows that the P.E. at point is completely converted into K.E. at point ‘M’. 

Energy
Conservation At Point ‘B’


At
point M the bob of Pendulum will not stop but due to inertia, the
bob will moves toward the point ‘B’. As the bob moves from ‘M’ to ‘B’, its
velocity gradually decreases but the height increases. At point ‘B’ velocity
of the bob will become zero. Thus K.E. at point ‘B’ = 0 but P.E. = max. P.E. = mgh. Energy total = K.E. + P.E. Energy total = 0 + mgh Energy total = mgh This shows that at point B total energy is again potential energy. 

CONCLUSION


^{ }Above analysis indicates that the total energy during the motion does not change. I.e. the motion of the bob of simple pendulum is according to the law of conservation of energy.  
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