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 fricitonless horizontal surface.
( iii) The work (W) done by the constant Force (F) for a displacement (s) in the same direction is ,
` W = Fs`
The constant force is given by the equation
F = ma
The third equation of motion can be written as
` v^(2) = u^(2) + 2as `
` a = ( v^(2) - u^(2))/( 2s)`
Sustituting for a in equation (2),
` F = m ((v^(2)-u^(2))/(2s))`
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)`
The expression for kinetic energy
(i) 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)`
(ii) Kinetic energy of the body is always positive . From equations (5) and (6)
` Delta KE = 1/2 mv^(2) - 1/2 mu^(2)`
Thus, W ` = DeltaKE `
(iii) The expression on the right hand side (RHS) of equation (7) is the change in kinetic enrgy , ` ( Delta KE)` of the body .
(iv) This implies that the work done by the force on the body changes the kinetic energy of the body . This is called work - kinetic energy theorem