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

Explanation

Work-kinetic energy theorem states that, work done by the force on the body changes the kinetic energy of the body.
Proof: 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 given by,
`W=Fs" "...(1)`
The constant force is given by the equation,
`F=ma" "...(2)`
We know that,
`v^(2)=u^(2)+2as`
`a=(v^(2)-u^(2))/(2s)`
Substituting for a in equation,
`F=m((v^(2)-u^(2))/(2s))" "...(3)`
Using equation (3), equation (1) can be written as
`W=m((v^(2))/(2s)s)-m((u^(2))/(2s)s)" "...(4)`
`W=(1)/(2)mv^(2)-(1)/(2)m u^(2)`
The expression for kinetic energy:
The term `((1)/(2)mv^(2))` in the above equation is the kinetic energy of the body of mass (m) moving with velocity (v).
`KE=(1)/(2)mv^(2)" "...(5)`
Kinetic energy of the body is always positive.
From equations (4) and (5) we get
`DeltaKE=(1)/(2)mv^(2)-(1)/(2)m u^(2)" "...(6)`
Thus, `W=DeltaKE`
Eg: In the case of uniform circular motion, the speed of the particle is constant and so the centripetal force does no work on the particle.