Question

The bob of a simple pendulum has imparted a velocity of 5m/s when it is at its mean position. To what maximum vertical height will it rise on reaching at its extreme position if 60% of its energy is lost in overcoming the friction of air?(Take g=$10m{s}^{-2}$ ).

Answer 1

Initial mechanical energy given to the bob, E = kinetic energy $=\frac{1}{2}m{v}^2$

Velocity of pendulum, $v=\frac{5m}{s}$

At the maximum height say ‘h’ the mechanical energy of the bob is only potential energy, so, $\text{PE = mgh}$ PE = mgh

But due to loss of energy in air resistance, only 40% of initial mechanical energy is converted to PE.

So, PE = 40% of KE

$mgh=0.4$ $\times \frac{1}{2}m{v}^2$

$m\left(10\right)h=0.4\times$ $\frac{1}{2}m\times 5^2$

$h=$ $0.4\times$ $\times \frac{25}{20}=0.5m$

So, maximum vertical height up to which it rise, $=0.5m$