The Bob of simple pendulum is imparted a velocity 5 m/s when it is at its mean position. To what maximum vertical height will it rise on reaching extreme position if 60% of its energy is lost in overcoming friction of air ? (g=10)

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Solution

Initial mechanical energy given to the bob, E = kinetic energy = ½ mv²
At the maximum height say ‘h’ the mechanical energy of the bob is only potential energy, so, PE = mgh
But due to loss of energy in air resistance, only 40% of initial mechanical energy is converted to PE.
So, PE = (40/100)KE
=> mgh = (0.4)(½ m)(5²)
=> h = (0.4)(0.5)(25)(1/10) = 0.5 m

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