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

Explanation

(i) It states that work done by the force acting on a body is equal to the change produced in the kintic energy of the body.
(ii) Consider a body of mass m at rest on a frictionless horizontal surface.
(iii) The work (W) done by the constant force (F) for displacement (s) in the same directions 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) " "` ....(3)
Substituting for a in equation (2),
`F=m((v^(2)-u^(2))/(2s)) " "` .....(4)
Substituting equation (4) in (1),
`W=m((v^(2))/(2s)s)-m((u^(2))/(2s)s)`
`W=(1)/(2)mv^(2)-(1)/(2)mu^(2) " "` ....(5)
The expression for kinetic energy :
(i) The term `((1)/(2)mv^(2))` in t equation (5) is the kinetic energy of the body of mass (m) moving with velocity (v).
`KE=(1)/(2)mv^(2) " "` ...(6)
(ii) Kinetic energy of the body is always positive. Form equations (5) and (6)
`Delta KE =(1)/(2)mv^(2)-(1)/(2)mu^(2) " "` ....(7)
Thus , `W=Delta KE`
(iii) The expression of the right hand side (RHS) of equation (7) is the change in kinetic energy `(Delta KE)` of the body.
(iv) This implies that the work done by the force on the body changes the energy of the body. This is called work - kinetic energy theroem.