Q42 of 54 Page 135

The total energy in an ideal simple pendulum is conserved. Calculated the energy in the different states of the pendulum and justify this statement.


In the position A, the total energy (E) of the pendulum is potential energy (U) and at point B the total energy of the pendulum is kinetic energy (K).


From the figure, x = l-lcosθ


A:


The total energy at A is given by,


E = U = mgx


E = mgl(1-cosθ)


B:


The total energy at B is given by,



The velocity of the bob of the pendulum at B is





So, the kinetic energy is




Hence, the total energy at A and B are same and we can say that the total energy of a pendulum remains constant.


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