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ENERGY- A system can do work provided it has energy. Energy (or stored work) is that physical quantity which enables a system to do work. With reference to sources and forms, energies have the form like heat, light, nuclear, mechanical etc. In this section, we restrict ourselves to mechanical energy which comprises two forms (i) kinetic energy (i) potential energy
Kinetic energy of a particle is the amount of work done by a force to change it's speed. Kinetic energy is the energy possess by a body due to its motion.
To get an expression for Kinetic energy, let us take an example shown in figure, The corresponding F.B.D. is shown in the figure below, which gives 8 m g and N=mg Now, the work done by the net external force along the surface is = ma x since cose = cos0 = 1, being the angle between a and x . m g Therefore, W=max
Therefore, W=max from kinematical equation for the velocities at A and B, we have where v is the velocity of the block at the position B This, ax Putting the value of ax' from equation 4 in equation 3, we have 2 2 2 2 The work done by the other two forces in F.B.D. for the displacement x are zero because N x = 0 and also mg . x = 0
2 The work done by the other two forces in F.B.D. for the displacement x are zero because N = 0 and also mg . x = 0. The equation (5) has two important consequences. (a) It establishes an important theorem related to work and energy, and (b) It gives the concept of kinetic energy. Firstly if Vo 0 i.e. initially the block is at rest, then 2 which implies kinetic energy is the energy possessed by the body in motion. If speed is zero, then kinetic energy is also zero.
Kinetic Energy in Terms of Momentum With reference to the adjacent figure, a body of mass m moving on a surface with a velocity v has a momentum, p=mv. Now, p . p-m2v2 = p2 The kinetic energy of the same body is, K=1/2 m v2 Therefore from equations (8) and (9), we have (10) 2 m
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