Question

The bob of a simple pendulum is 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 percent of its energy is lost in overcoming the friction of air? (take g = 10ms^-2).

Answer 1

"We Know that initial Kinetic energy is 1/2 × Mass × (Square of velocity).  

Let's assume that the bob reaches the height h.  

At this particular height, the mechanical energy of the bob is said to be the potential energy.  

Therefore, Potential Energy (PE) = mgh

But, due to resistance offered by air, there is a chance of losing energy.  

Given, 60% of energy is lost in overcoming the friction of air.  

Therefore only 40% of mechanical energy gets converted to potential energy.

Therefore, PE = (40/100) K.E

mgh = (0.4) (½ m) (5²)

h = (0.4) (0.5) (25) (1/10)

h = 0.5m