ENERGY
The energy of a body is its capacity for doing work. In mechanics the two kinds of energies are, Potential and kinetic.
The capacity of doing work in virute of position is known as the potential energy of the body. A body of mass "m" kg at a hight of "h" m. Above a given datum possesses "mh" m. Kg of energy, and by allowing the mass to fall, this work can be utilised. The stone on the roof, water stored up in a overhead tank, a wound spring and a mass of compressed gas are a few examples of cases having potential energy.
kinetic energy of a body is that due to its motion. A sationary body has no kinetic energy but may or may not possess potential energy, a moving body possess potential energy. The motion of body may be one of translation or rotation and the kinetic energy (K.E) will be K.E of translation or rotation respectively or both if the body has combined motion of translation and rotation.
Consider a body of mass "m" kg. Moving with a velocity of "v" m./sec. It has a kinetic energy of translation and the measure of this kinetic energy will be the amount of work whicy it will give up before coming to rest. Imagine a retarding force of "P" kg. being applied to it so that it comes to rest in "S" m. Then, the work absorbed by 'P' will be =PS m. Kg. Since the body has now come to rest, this is the measure of its K.E of translation.
Now, P = ma/g where, 'a' is the retardation.
Also since the body has come to rest,
V² = 0+2aS
Therfore S = v²/2a
P×S = ma/g×v²/2a= mv²/2g (m).kg.
The K.E. of translation is,
therefore, mv²/2g(m).Kg.
Thus, we find that the K.E depends upon the weight ofbody and the sqare of its velocity, which means if velocitu is doubled, the energy is increased four times, not twice.
When body is accelerated, force is required to produce the acceleration and hence work is done. The work done olin this manner is equal to change of K.E in the body. Considering a force 'P' acting on a mass 'm' and producing acceleration "a" , the velocity acquiredwhen a distance 'S' has been transversed is found from
v² = u²+2as.
Multyplying throughout by m/2g and transposing,
mv²/2g — mu²/2g = 2aSm/2g
Therefore
mv²/2g — mu²/2g = ma/g×S = P×S
Therfore (P = ma/g)
The left hand side of the equation represents the change of K.E and the right hand side the work done.
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