The Darjeeling Himalayan Railway (DHR) was built by the
British between 1789 and 1881 connecting the cities of Siliguri and Darjeeling
in West Bengal. It was constructed with some ingenious engineering concepts,
including Zig-Zag paths and looping over its own line.
The concept of potential energy plays an important role,
especially in trains coming down the hill from Darjeeling to Siliguri.
Attached below is a picture which shows the heights of the
different stations in the line.
Potential energy is defined as the energy possessed by a
body by virtue of its position. It is more like the respect the aristocracy and
the noblemen got in the olden times by virtue of their position.
In other words,
P.E.=mgh
Where
P.E. = Potential
Energy possessed by the body
m= Mass of the body
g= Acceleration of
the body
h=height of the body
with respect to sea level.
Let us calculate the Potential Energy of the Toy Train at
Ghum, the highest point in the line.
(Assuming the mass of the train is about 40 tonnes, or 4 x104
kg)
(Height of Ghum is 7407 ft, or 2257.654 m)
(g=9.8 m/s2)
P.E. = mgh
= (4 x104
kg)(9.8 m/s2)( 2257.654 m)
=885000368 kg
m2/s2 or 8.85 x 108 Joules.
That is close to the energy possessed by a man weighing 40
kg moving at 16,740 km/h!
The potential energy referred to here is otherwise known as
gravitational potential energy, i.e. the energy acquired by a body due to
climbing against gravity.
