State and explain work energy principle. Mention any three examples for it.

Explanation

(a) Work and energy are equivalents. This is true in the case of kinetic energy also. To prove this, let us consider a body of mass· m at rest on a frictionless horizontal surface. The work (W) done by the constant force (F) for a displacement (s) in the same direction is,
` W = Fs` ...(1)
The constant force is given by the equation,
F = ma ....(2)
The third equation of motion can be written as,
` v^2 = u^2 + 2as`
` a = (v^2 - u^2)/(2s)`
Substituting for a in equation (2),
` F = m ( (v^2 - u^2) /(2s) )` ....(4)
Substituting equation (3) in (I)
`w = m ( (v^2)/(2s) s ) - m ( (u^2)/(2s) s )`
` W = 1/2 mv^2 - 1/2 mu^2` ....(5)
(b) (i) If the work done by the force on the body is positive then its kinetic energy increases (ii) If the work done by the force on the body is negative then its kinetic energy decreases . (iii) If there ·is no work done by the force on the body then then there is no change in its kinetic energy, which means that the body has moved .at constant speed provided its mass remains constant. (iv) When a particle moves with constant speed in a circle, there is no change in the kinetic energy of the particle . So according to work energy principle, the work done by centripetal force is zero.