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The following problems are based on the topic Work Energy Theorem.

Example WET.1: An Object of mass m is tied to a string of length l and a variable force F is applied on it which brings the string gradually at angle θwith the vertical. Find the work done by the force F.

Solution WET.1: STEP 1: Draw a rough sketch if possible STEP 2: Solution In this case three forces are acting on the object:

  1. Tension (T)
  2. weight (mg) and
  3. applied force (F)

Using Work Energy Theorem,

$ W_{net} = \Delta KE $
or $ W_T + W_{mg} + W_F = 0 $
as $ \Delta KE = 0 $
because $ K_i = K_f = 0 $

Further, $ W_T = 0 $, as tension is always perpendicular to displacement. $ W_{mg} = -mgh $ or $ W_{mg} = - mgl(l - \cos{\theta} ) $

NOTE: the applied force F is variable. So, if we do not apply Work energy theorem here we will have to use method of integration.