The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1 m, what is the speed with which the bob reaches the lower most point, given that it dissipates 10% of the initial energy against air resistance ?

The bob of a pendulum is released from a horizontal position. If the l

1.	The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1 m, what is the speed with which the bob reaches the lower most point, given that it dissipates 10% of the initial energy against air resistance ?
Answer» Solution :When the BOB is the horizontal POSITION its POTENTIAL energy = MGH. When it reaches the lowest position, its kinetic energy `= (1)/(2) mv^(2)`. As part of the INITIAL energy is dissipated against air resistance, by the principle of conservation of energy. Potential energy in the horizontal position = Kinetic energy at the lower most point + Energy dissipated `mgh = (1)/(2) mv^(2) + ((10)/(100))` initial energy `mgh = (1)/(2) mv^(2) + 0.1` mgh 0.9 mgh `= (1)/(2) mv^(2) rArr v = sqrt(2 xx 0.9 xx g xx h)` `= sqrt(2 xx 0.9 xx 9.8 xx 1) (because h = l) = 4.2 ms^(-1)`