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Question

Under what conditions is the work done i) maximum and ii) minimum?


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Solution

Step 1: Work:

  1. Work done is defined as the scalar product of force and the displacement.
  2. It is a scalar quantity.
  3. The unit of work is Joule.

Step 2: Condition for the maximum work:

Work, W=Fscosθ

Where, force is F, displacement is s and angle between the force and the displacement is θ.

Since for a given system, Force and displacement can not change. So, for maximum work cosθ should be maximum.

cosθmax=1cosθmax=cos0θ=0

Step 3: Condition for minimum work:

Since for a given system, Force and displacement can not change. So, for minimum work cosθ should be minimum.

cosθmin=0cosθmin=cos90θ=90

Hence, the required condition for maximum work is θ=0 and condition for minimum work is θ=90.


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