In which of the following cases is the work done negative?
Force and displacement are between 90° and 180°
Work done is defined as \(W = F \cdot s \cdot \cos\theta\), where \(\theta\) is the angle between the force and the displacement.
The sign of the work depends entirely on \(\cos\theta\), since force magnitude and displacement magnitude are always positive.
When \(\theta\) lies between 90° and 180°, \(\cos\theta\) is negative, so the work done becomes negative (the force opposes the motion, e.g. friction).
For 0° to 90°, \(\cos\theta\) is positive (positive work); at exactly 90° the force and displacement are perpendicular and \(\cos 90° = 0\), giving zero work.
Hence, the work done is negative when the force and displacement are between 90° and 180°.
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