# Work Energy Theorem/Problems

## < Work Energy Theorem

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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.