Q. 184.6( 24 Votes )

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?

Answer :

Given,

Length of the pendulum, l = 1.5 m


Energy dissipated against air resistance, E = 5%


Let m be the mass of the bob and v be its velocity at the lowermost point.


At the extreme end:


Potential energy of the bob, P = mgl


Kinetic energy of the bob, K = 0 ( bob is at rest)


Total energy of bob, E = P + E


E = mgl ……………(1)


At the lowermost point:


Potential energy of the bob, P = 0


Kinetic energy of the bob, K = (1/2)mv2


Total energy of the bob, E = P + K


E = (1/2)mv2


During the motion from an extreme end to the lowermost point, the bob loses 5% of its energy, i.e., it has 95% of the energy.


So, (1/2)mv2 = (95/100)mgl


v2 = 95gl/50


v =


v =


v = 5.28 m s-1


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