Work, Power and Energy
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Question : 18
Total: 30
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?
Solution:
Length of pendulum h = 1.5 m
Let m be mass of the bob, then potential energy of the bob at A,
m g h = m × 9.8 × 1.5 J
On reaching the lowest point B, the bob will acquire an equal amount ofkinetic energy. But as 5% of energy is lost against the air friction.
Energy converted= 95 % ( m g h )
If v is the velocity acquired by the bob at the point B, then
K . E . =
m v 2 =
m g h
v = √
× 2 × g h = √
× 2 × 9.8 × 1.5 = 5.285 m s − 1
Let m be mass of the bob, then potential energy of the bob at A,
On reaching the lowest point B, the bob will acquire an equal amount ofkinetic energy. But as 5% of energy is lost against the air friction.
Energy converted
If v is the velocity acquired by the bob at the point B, then
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