Advertisement Remove all ads

Notions of Work and Kinetic Energy: the Work-Energy Theorem

Advertisement Remove all ads



  • Work-Energy Theorem


Notions of Work and Kinetic Energy

“The work-energy theorem states that the change in kinetic energy of a particle is equal to the work done on it by the net force.”

  • Kf – Ki = W
    where Kf is the final Kinetic Energy and Ki is the initial Kinetic Energy

  • We know the equation in 3D: v2 – u2 = 2 a.d (where u - initial velocity, v - final velocity, a -acceleration, d - displacement)
    Now multiplying the equation by m/2 we have,

    ½ mv2 – ½ mu2 = ma.d

    ½ mv2 – ½ mu2 = F.d (Since ma = F)

The Work-Energy Theorem for a Variable Force

The time rate for change of kinetic energy
`(dK)/(dt)=d/(dt)(1/2 mv^2)`
       `=Fv`           ...(from Newton's Second Law)
   `dK=F dx`
Integrating from initial position (xi) to final position (xf), we have
   `∫_(K_i)^(K_f) dK=∫_(x_i)^(x_f)F dx`
where, Kt and Kf are the initial and final kinetic energies corresponding to xi and xf,
or `K_f-K_i=∫_(x_i)^(x_f) F dx`
From earlier proved equation, it follows that
     `K_f-K_i =W`
Thus, the W.E. theorem is proved for a variable force. 

Regarding the work-energy theorem it is worth noting that
(i) If Wnet is positive, then Kf – Ki = positive, i.e., Kf > Ki or kinetic energy will increase and vice-versa.
(ii) This theorem can be applied to non-inertial frames also. In a non-inertial frame it can be written as:

Work done by all the forces (including the Pseudo force) = change in kinetic energy in non-inertial frame.

If you would like to contribute notes or other learning material, please submit them using the button below.
Advertisement Remove all ads

View all notifications

      Forgot password?
View in app×